Properties

Label 7650.2.a
Level $7650$
Weight $2$
Character orbit 7650.a
Rep. character $\chi_{7650}(1,\cdot)$
Character field $\Q$
Dimension $128$
Newform subspaces $94$
Sturm bound $3240$
Trace bound $29$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 7650 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7650.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 94 \)
Sturm bound: \(3240\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(19\), \(23\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7650))\).

Total New Old
Modular forms 1668 128 1540
Cusp forms 1573 128 1445
Eisenstein series 95 0 95

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)\(17\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(9\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(10\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(10\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(10\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(11\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(12\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(8\)
Plus space\(+\)\(55\)
Minus space\(-\)\(73\)

Trace form

\( 128 q + 128 q^{4} - 4 q^{7} + O(q^{10}) \) \( 128 q + 128 q^{4} - 4 q^{7} + 2 q^{11} - 4 q^{13} - 4 q^{14} + 128 q^{16} + 2 q^{17} + 16 q^{19} - 6 q^{22} - 8 q^{23} + 4 q^{26} - 4 q^{28} + 10 q^{29} + 20 q^{31} + 2 q^{34} + 30 q^{37} - 16 q^{38} - 4 q^{41} + 12 q^{43} + 2 q^{44} + 16 q^{46} + 16 q^{47} + 160 q^{49} - 4 q^{52} - 12 q^{53} - 4 q^{56} + 10 q^{58} + 36 q^{59} + 34 q^{61} + 20 q^{62} + 128 q^{64} + 4 q^{67} + 2 q^{68} + 72 q^{71} - 8 q^{73} - 34 q^{74} + 16 q^{76} - 24 q^{77} + 64 q^{79} + 12 q^{82} - 12 q^{83} - 4 q^{86} - 6 q^{88} + 56 q^{89} + 40 q^{91} - 8 q^{92} + 24 q^{94} + 44 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7650))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5 17
7650.2.a.a 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.a \(-1\) \(0\) \(0\) \(-5\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-5q^{7}-q^{8}-5q^{11}+5q^{14}+\cdots\)
7650.2.a.b 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.g \(-1\) \(0\) \(0\) \(-5\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-5q^{7}-q^{8}+q^{11}+2q^{13}+\cdots\)
7650.2.a.c 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.q \(-1\) \(0\) \(0\) \(-4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{7}-q^{8}-2q^{11}-2q^{13}+\cdots\)
7650.2.a.d 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.p \(-1\) \(0\) \(0\) \(-4\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{7}-q^{8}+2q^{11}-6q^{13}+\cdots\)
7650.2.a.e 7650.a 1.a $1$ $61.086$ \(\Q\) None 510.2.d.a \(-1\) \(0\) \(0\) \(-4\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{7}-q^{8}+2q^{11}+4q^{13}+\cdots\)
7650.2.a.f 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.f \(-1\) \(0\) \(0\) \(-3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{7}-q^{8}+5q^{11}-4q^{13}+\cdots\)
7650.2.a.g 7650.a 1.a $1$ $61.086$ \(\Q\) None 170.2.a.a \(-1\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{7}-q^{8}-6q^{11}-2q^{13}+\cdots\)
7650.2.a.h 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.h \(-1\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{7}-q^{8}-2q^{11}+2q^{14}+\cdots\)
7650.2.a.i 7650.a 1.a $1$ $61.086$ \(\Q\) None 170.2.a.c \(-1\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{7}-q^{8}-5q^{13}+2q^{14}+\cdots\)
7650.2.a.j 7650.a 1.a $1$ $61.086$ \(\Q\) None 102.2.a.b \(-1\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{7}-q^{8}-2q^{13}+2q^{14}+\cdots\)
7650.2.a.k 7650.a 1.a $1$ $61.086$ \(\Q\) None 510.2.a.a \(-1\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{7}-q^{8}+4q^{11}-4q^{13}+\cdots\)
7650.2.a.l 7650.a 1.a $1$ $61.086$ \(\Q\) None 170.2.a.d \(-1\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{7}-q^{8}+4q^{11}+3q^{13}+\cdots\)
7650.2.a.m 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.m \(-1\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{7}-q^{8}+6q^{11}+4q^{13}+\cdots\)
7650.2.a.n 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.n \(-1\) \(0\) \(0\) \(-1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}-4q^{13}+\cdots\)
7650.2.a.o 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.m \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}+4q^{13}+\cdots\)
7650.2.a.p 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.e \(-1\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}-6q^{11}-2q^{13}+\cdots\)
7650.2.a.q 7650.a 1.a $1$ $61.086$ \(\Q\) None 1530.2.d.a \(-1\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}+q^{16}+q^{17}-4q^{19}+\cdots\)
7650.2.a.r 7650.a 1.a $1$ $61.086$ \(\Q\) None 1530.2.d.a \(-1\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}+q^{16}+q^{17}-4q^{19}+\cdots\)
7650.2.a.s 7650.a 1.a $1$ $61.086$ \(\Q\) None 170.2.c.a \(-1\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{8}+6q^{11}-3q^{13}+\cdots\)
7650.2.a.t 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.k \(-1\) \(0\) \(0\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{11}+4q^{13}+\cdots\)
7650.2.a.u 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.n \(-1\) \(0\) \(0\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{11}+4q^{13}+\cdots\)
7650.2.a.v 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.j \(-1\) \(0\) \(0\) \(1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-2q^{13}+\cdots\)
7650.2.a.w 7650.a 1.a $1$ $61.086$ \(\Q\) None 850.2.a.a \(-1\) \(0\) \(0\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}+4q^{11}-3q^{13}+\cdots\)
7650.2.a.x 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.m \(-1\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{7}-q^{8}-6q^{11}-4q^{13}+\cdots\)
7650.2.a.y 7650.a 1.a $1$ $61.086$ \(\Q\) None 510.2.a.b \(-1\) \(0\) \(0\) \(2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{7}-q^{8}-4q^{11}-2q^{14}+\cdots\)
7650.2.a.z 7650.a 1.a $1$ $61.086$ \(\Q\) None 102.2.a.a \(-1\) \(0\) \(0\) \(2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{7}-q^{8}+6q^{13}-2q^{14}+\cdots\)
7650.2.a.ba 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.h \(-1\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{7}-q^{8}+2q^{11}-2q^{14}+\cdots\)
7650.2.a.bb 7650.a 1.a $1$ $61.086$ \(\Q\) None 1530.2.a.e \(-1\) \(0\) \(0\) \(2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{7}-q^{8}+2q^{11}-2q^{14}+\cdots\)
7650.2.a.bc 7650.a 1.a $1$ $61.086$ \(\Q\) None 170.2.a.b \(-1\) \(0\) \(0\) \(2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{7}-q^{8}+2q^{11}+6q^{13}+\cdots\)
7650.2.a.bd 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.a \(-1\) \(0\) \(0\) \(3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{7}-q^{8}+3q^{11}+4q^{13}+\cdots\)
7650.2.a.be 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.h \(-1\) \(0\) \(0\) \(3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{7}-q^{8}+5q^{11}-2q^{13}+\cdots\)
7650.2.a.bf 7650.a 1.a $1$ $61.086$ \(\Q\) None 1530.2.a.a \(-1\) \(0\) \(0\) \(4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+4q^{7}-q^{8}-2q^{11}+6q^{13}+\cdots\)
7650.2.a.bg 7650.a 1.a $1$ $61.086$ \(\Q\) None 850.2.a.c \(-1\) \(0\) \(0\) \(5\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+5q^{7}-q^{8}-4q^{11}-3q^{13}+\cdots\)
7650.2.a.bh 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.a \(-1\) \(0\) \(0\) \(5\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+5q^{7}-q^{8}+5q^{11}-5q^{14}+\cdots\)
7650.2.a.bi 7650.a 1.a $1$ $61.086$ \(\Q\) None 850.2.a.c \(1\) \(0\) \(0\) \(-5\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-5q^{7}+q^{8}-4q^{11}+3q^{13}+\cdots\)
7650.2.a.bj 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.a \(1\) \(0\) \(0\) \(-5\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-5q^{7}+q^{8}+5q^{11}-5q^{14}+\cdots\)
7650.2.a.bk 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.a \(1\) \(0\) \(0\) \(-3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{7}+q^{8}+3q^{11}-4q^{13}+\cdots\)
7650.2.a.bl 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.h \(1\) \(0\) \(0\) \(-3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{7}+q^{8}+5q^{11}+2q^{13}+\cdots\)
7650.2.a.bm 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.m \(1\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{7}+q^{8}-6q^{11}+4q^{13}+\cdots\)
7650.2.a.bn 7650.a 1.a $1$ $61.086$ \(\Q\) None 510.2.a.d \(1\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{7}+q^{8}-4q^{13}-2q^{14}+\cdots\)
7650.2.a.bo 7650.a 1.a $1$ $61.086$ \(\Q\) None 170.2.a.e \(1\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{7}+q^{8}+q^{13}-2q^{14}+\cdots\)
7650.2.a.bp 7650.a 1.a $1$ $61.086$ \(\Q\) None 510.2.a.g \(1\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{7}+q^{8}+4q^{13}-2q^{14}+\cdots\)
7650.2.a.bq 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.h \(1\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{7}+q^{8}+2q^{11}-2q^{14}+\cdots\)
7650.2.a.br 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.k \(1\) \(0\) \(0\) \(-1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}-4q^{13}+\cdots\)
7650.2.a.bs 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.n \(1\) \(0\) \(0\) \(-1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}-4q^{13}+\cdots\)
7650.2.a.bt 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.j \(1\) \(0\) \(0\) \(-1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+2q^{13}+\cdots\)
7650.2.a.bu 7650.a 1.a $1$ $61.086$ \(\Q\) None 850.2.a.a \(1\) \(0\) \(0\) \(-1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}+4q^{11}+3q^{13}+\cdots\)
7650.2.a.bv 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.e \(1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-6q^{11}+2q^{13}+\cdots\)
7650.2.a.bw 7650.a 1.a $1$ $61.086$ \(\Q\) None 510.2.a.f \(1\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-4q^{11}-2q^{13}+\cdots\)
7650.2.a.bx 7650.a 1.a $1$ $61.086$ \(\Q\) None 510.2.a.e \(1\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-4q^{11}+2q^{13}+\cdots\)
7650.2.a.by 7650.a 1.a $1$ $61.086$ \(\Q\) None 1530.2.d.a \(1\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+q^{16}-q^{17}-4q^{19}+\cdots\)
7650.2.a.bz 7650.a 1.a $1$ $61.086$ \(\Q\) None 1530.2.d.a \(1\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+q^{16}-q^{17}-4q^{19}+\cdots\)
7650.2.a.ca 7650.a 1.a $1$ $61.086$ \(\Q\) None 102.2.a.c \(1\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+4q^{11}+2q^{13}+\cdots\)
7650.2.a.cb 7650.a 1.a $1$ $61.086$ \(\Q\) None 170.2.c.a \(1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+6q^{11}+3q^{13}+\cdots\)
7650.2.a.cc 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.m \(1\) \(0\) \(0\) \(1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}+3q^{11}-4q^{13}+\cdots\)
7650.2.a.cd 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.n \(1\) \(0\) \(0\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{7}+q^{8}+3q^{11}+4q^{13}+\cdots\)
7650.2.a.ce 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.h \(1\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{7}+q^{8}-2q^{11}+2q^{14}+\cdots\)
7650.2.a.cf 7650.a 1.a $1$ $61.086$ \(\Q\) None 1530.2.a.e \(1\) \(0\) \(0\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{7}+q^{8}-2q^{11}+2q^{14}+\cdots\)
7650.2.a.cg 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.m \(1\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{7}+q^{8}+6q^{11}-4q^{13}+\cdots\)
7650.2.a.ch 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.f \(1\) \(0\) \(0\) \(3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{7}+q^{8}+5q^{11}+4q^{13}+\cdots\)
7650.2.a.ci 7650.a 1.a $1$ $61.086$ \(\Q\) None 34.2.a.a \(1\) \(0\) \(0\) \(4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{7}+q^{8}-6q^{11}-2q^{13}+\cdots\)
7650.2.a.cj 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.q \(1\) \(0\) \(0\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{7}+q^{8}-2q^{11}+2q^{13}+\cdots\)
7650.2.a.ck 7650.a 1.a $1$ $61.086$ \(\Q\) None 510.2.d.a \(1\) \(0\) \(0\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{7}+q^{8}+2q^{11}-4q^{13}+\cdots\)
7650.2.a.cl 7650.a 1.a $1$ $61.086$ \(\Q\) None 1530.2.a.a \(1\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{7}+q^{8}+2q^{11}+6q^{13}+\cdots\)
7650.2.a.cm 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.p \(1\) \(0\) \(0\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{7}+q^{8}+2q^{11}+6q^{13}+\cdots\)
7650.2.a.cn 7650.a 1.a $1$ $61.086$ \(\Q\) None 510.2.a.c \(1\) \(0\) \(0\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{7}+q^{8}+4q^{11}+2q^{13}+\cdots\)
7650.2.a.co 7650.a 1.a $1$ $61.086$ \(\Q\) None 7650.2.a.a \(1\) \(0\) \(0\) \(5\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+5q^{7}+q^{8}-5q^{11}+5q^{14}+\cdots\)
7650.2.a.cp 7650.a 1.a $1$ $61.086$ \(\Q\) None 2550.2.a.g \(1\) \(0\) \(0\) \(5\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+5q^{7}+q^{8}+q^{11}-2q^{13}+\cdots\)
7650.2.a.cq 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{6}) \) None 306.2.a.e \(-2\) \(0\) \(0\) \(-4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-2+\beta )q^{7}-q^{8}-2\beta q^{11}+\cdots\)
7650.2.a.cr 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{2}) \) None 7650.2.a.cr \(-2\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta )q^{7}-q^{8}-q^{11}+\cdots\)
7650.2.a.cs 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{5}) \) None 1530.2.a.q \(-2\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1-\beta )q^{7}-q^{8}+2q^{11}+\cdots\)
7650.2.a.ct 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{6}) \) None 510.2.d.c \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{7}-q^{8}+2\beta q^{11}+\cdots\)
7650.2.a.cu 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{6}) \) None 510.2.a.h \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{7}-q^{8}+(-2-\beta )q^{13}+\cdots\)
7650.2.a.cv 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{33}) \) None 2550.2.a.bg \(-2\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{7}-q^{8}+(-2+\beta )q^{11}+\cdots\)
7650.2.a.cw 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{2}) \) None 850.2.a.m \(-2\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta )q^{7}-q^{8}-2q^{11}+\cdots\)
7650.2.a.cx 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{5}) \) None 510.2.d.b \(-2\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta )q^{7}-q^{8}-2q^{11}+\cdots\)
7650.2.a.cy 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{2}) \) None 7650.2.a.cr \(-2\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta )q^{7}-q^{8}+q^{11}+\cdots\)
7650.2.a.cz 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{6}) \) None 306.2.a.e \(2\) \(0\) \(0\) \(-4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-2+\beta )q^{7}+q^{8}+2\beta q^{11}+\cdots\)
7650.2.a.da 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{5}) \) None 510.2.d.b \(2\) \(0\) \(0\) \(-2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1-\beta )q^{7}+q^{8}-2q^{11}+\cdots\)
7650.2.a.db 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{5}) \) None 1530.2.a.q \(2\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1-\beta )q^{7}+q^{8}-2q^{11}+\cdots\)
7650.2.a.dc 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{2}) \) None 850.2.a.m \(2\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta )q^{7}+q^{8}-2q^{11}+\cdots\)
7650.2.a.dd 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{2}) \) None 7650.2.a.cr \(2\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1+\beta )q^{7}+q^{8}+q^{11}+\cdots\)
7650.2.a.de 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{17}) \) None 170.2.a.f \(2\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2\beta q^{7}+q^{8}+4q^{11}+\cdots\)
7650.2.a.df 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{33}) \) None 2550.2.a.bg \(2\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-\beta q^{7}+q^{8}+(-2+\beta )q^{11}+\cdots\)
7650.2.a.dg 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{6}) \) None 510.2.d.c \(2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{7}+q^{8}-2\beta q^{11}+\cdots\)
7650.2.a.dh 7650.a 1.a $2$ $61.086$ \(\Q(\sqrt{2}) \) None 7650.2.a.cr \(2\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta )q^{7}+q^{8}-q^{11}+\cdots\)
7650.2.a.di 7650.a 1.a $3$ $61.086$ 3.3.148.1 None 1530.2.d.h \(-3\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{2}q^{7}-q^{8}-4q^{11}+\cdots\)
7650.2.a.dj 7650.a 1.a $3$ $61.086$ 3.3.568.1 None 170.2.c.b \(-3\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(\beta _{1}+\beta _{2})q^{7}-q^{8}-2q^{11}+\cdots\)
7650.2.a.dk 7650.a 1.a $3$ $61.086$ 3.3.148.1 None 1530.2.d.h \(-3\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta _{2}q^{7}-q^{8}+4q^{11}+\cdots\)
7650.2.a.dl 7650.a 1.a $3$ $61.086$ 3.3.568.1 None 510.2.d.d \(-3\) \(0\) \(0\) \(6\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(2+\beta _{1})q^{7}-q^{8}+(-1+\cdots)q^{11}+\cdots\)
7650.2.a.dm 7650.a 1.a $3$ $61.086$ 3.3.568.1 None 510.2.d.d \(3\) \(0\) \(0\) \(-6\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-2-\beta _{1})q^{7}+q^{8}+(-1+\cdots)q^{11}+\cdots\)
7650.2.a.dn 7650.a 1.a $3$ $61.086$ 3.3.148.1 None 1530.2.d.h \(3\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-\beta _{2}q^{7}+q^{8}-4q^{11}+\cdots\)
7650.2.a.do 7650.a 1.a $3$ $61.086$ 3.3.568.1 None 170.2.c.b \(3\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-\beta _{1}-\beta _{2})q^{7}+q^{8}+\cdots\)
7650.2.a.dp 7650.a 1.a $3$ $61.086$ 3.3.148.1 None 1530.2.d.h \(3\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta _{2}q^{7}+q^{8}+4q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7650))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7650)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(306))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(425))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(765))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(850))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1275))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1530))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2550))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3825))\)\(^{\oplus 2}\)