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Properties

Label 8325.2.a
Level $8325$
Weight $2$
Character orbit 8325.a
Rep. character $\chi_{8325}(1,\cdot)$
Character field $\Q$
Dimension $285$
Newform subspaces $76$
Sturm bound $2280$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 8325 = 3^{2} \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8325.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 76 \)
Sturm bound: \(2280\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8325))\).

Total New Old
Modular forms 1164 285 879
Cusp forms 1117 285 832
Eisenstein series 47 0 47

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

\(3\)\(5\)\(37\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(24\)
\(+\)\(+\)\(-\)\(-\)\(30\)
\(+\)\(-\)\(+\)\(-\)\(32\)
\(+\)\(-\)\(-\)\(+\)\(28\)
\(-\)\(+\)\(+\)\(-\)\(42\)
\(-\)\(+\)\(-\)\(+\)\(39\)
\(-\)\(-\)\(+\)\(+\)\(44\)
\(-\)\(-\)\(-\)\(-\)\(46\)
Plus space\(+\)\(135\)
Minus space\(-\)\(150\)

Trace form

\( 285 q - q^{2} + 289 q^{4} + 2 q^{7} - 15 q^{8} + O(q^{10}) \) \( 285 q - q^{2} + 289 q^{4} + 2 q^{7} - 15 q^{8} + 2 q^{11} + 8 q^{13} - 2 q^{14} + 297 q^{16} + 14 q^{19} + 2 q^{22} - 4 q^{23} - 18 q^{26} + 4 q^{28} + 22 q^{29} + 12 q^{31} - 11 q^{32} - 10 q^{34} + q^{37} + 4 q^{38} - 4 q^{41} + 18 q^{43} - 20 q^{44} - 28 q^{46} + 14 q^{47} + 291 q^{49} + 10 q^{52} + 12 q^{53} - 28 q^{56} - 10 q^{58} - 44 q^{59} - 2 q^{61} - 32 q^{62} + 301 q^{64} + 16 q^{67} + 46 q^{68} + 2 q^{71} + 48 q^{73} + 5 q^{74} + 4 q^{76} - 46 q^{77} - 18 q^{79} + 4 q^{82} + 6 q^{83} + 8 q^{86} - 36 q^{88} + 32 q^{89} - 34 q^{91} - 72 q^{92} - 94 q^{94} + 54 q^{97} - 7 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8325))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 37
8325.2.a.a 8325.a 1.a $1$ $66.475$ \(\Q\) None 1665.2.a.a \(-2\) \(0\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-4q^{7}-q^{13}+8q^{14}+\cdots\)
8325.2.a.b 8325.a 1.a $1$ $66.475$ \(\Q\) None 8325.2.a.b \(-2\) \(0\) \(0\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{7}-6q^{11}-7q^{13}+\cdots\)
8325.2.a.c 8325.a 1.a $1$ $66.475$ \(\Q\) None 2775.2.a.b \(-2\) \(0\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{7}+5q^{13}+2q^{14}+\cdots\)
8325.2.a.d 8325.a 1.a $1$ $66.475$ \(\Q\) None 555.2.c.a \(-2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+2q^{11}+q^{13}-4q^{16}+\cdots\)
8325.2.a.e 8325.a 1.a $1$ $66.475$ \(\Q\) None 37.2.a.a \(-2\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{7}+5q^{11}+2q^{13}+\cdots\)
8325.2.a.f 8325.a 1.a $1$ $66.475$ \(\Q\) None 8325.2.a.b \(-2\) \(0\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{7}+6q^{11}+7q^{13}+\cdots\)
8325.2.a.g 8325.a 1.a $1$ $66.475$ \(\Q\) None 185.2.a.a \(-2\) \(0\) \(0\) \(5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+5q^{7}-3q^{11}+2q^{13}+\cdots\)
8325.2.a.h 8325.a 1.a $1$ $66.475$ \(\Q\) None 333.2.a.a \(-1\) \(0\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+4q^{7}+3q^{8}+4q^{11}+\cdots\)
8325.2.a.i 8325.a 1.a $1$ $66.475$ \(\Q\) None 2775.2.a.c \(0\) \(0\) \(0\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-3q^{7}-4q^{11}-5q^{13}+4q^{16}+\cdots\)
8325.2.a.j 8325.a 1.a $1$ $66.475$ \(\Q\) None 8325.2.a.j \(0\) \(0\) \(0\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-3q^{7}-4q^{11}+q^{13}+4q^{16}+\cdots\)
8325.2.a.k 8325.a 1.a $1$ $66.475$ \(\Q\) None 8325.2.a.j \(0\) \(0\) \(0\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-3q^{7}+4q^{11}+q^{13}+4q^{16}+\cdots\)
8325.2.a.l 8325.a 1.a $1$ $66.475$ \(\Q\) None 1665.2.c.b \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-2q^{7}-6q^{11}-q^{13}+4q^{16}+\cdots\)
8325.2.a.m 8325.a 1.a $1$ $66.475$ \(\Q\) None 555.2.a.b \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-2q^{7}+q^{13}+4q^{16}+6q^{17}+\cdots\)
8325.2.a.n 8325.a 1.a $1$ $66.475$ \(\Q\) None 1665.2.c.b \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-2q^{7}+6q^{11}-q^{13}+4q^{16}+\cdots\)
8325.2.a.o 8325.a 1.a $1$ $66.475$ \(\Q\) None 2775.2.a.e \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{7}+2q^{11}+q^{13}+4q^{16}+\cdots\)
8325.2.a.p 8325.a 1.a $1$ $66.475$ \(\Q\) None 37.2.a.b \(0\) \(0\) \(0\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{7}-3q^{11}+4q^{13}+4q^{16}+\cdots\)
8325.2.a.q 8325.a 1.a $1$ $66.475$ \(\Q\) None 2775.2.a.e \(0\) \(0\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{7}+2q^{11}-q^{13}+4q^{16}+\cdots\)
8325.2.a.r 8325.a 1.a $1$ $66.475$ \(\Q\) None 1665.2.c.b \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+2q^{7}-6q^{11}+q^{13}+4q^{16}+\cdots\)
8325.2.a.s 8325.a 1.a $1$ $66.475$ \(\Q\) None 555.2.a.a \(0\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+2q^{7}-4q^{11}-5q^{13}+4q^{16}+\cdots\)
8325.2.a.t 8325.a 1.a $1$ $66.475$ \(\Q\) None 1665.2.c.b \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+2q^{7}+6q^{11}+q^{13}+4q^{16}+\cdots\)
8325.2.a.u 8325.a 1.a $1$ $66.475$ \(\Q\) None 8325.2.a.j \(0\) \(0\) \(0\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{7}-4q^{11}-q^{13}+4q^{16}+\cdots\)
8325.2.a.v 8325.a 1.a $1$ $66.475$ \(\Q\) None 2775.2.a.c \(0\) \(0\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{7}-4q^{11}+5q^{13}+4q^{16}+\cdots\)
8325.2.a.w 8325.a 1.a $1$ $66.475$ \(\Q\) None 8325.2.a.j \(0\) \(0\) \(0\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{7}+4q^{11}-q^{13}+4q^{16}+\cdots\)
8325.2.a.x 8325.a 1.a $1$ $66.475$ \(\Q\) None 185.2.a.b \(0\) \(0\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{7}+5q^{11}-4q^{13}+4q^{16}+\cdots\)
8325.2.a.y 8325.a 1.a $1$ $66.475$ \(\Q\) None 185.2.a.c \(1\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{7}-3q^{8}+2q^{13}+\cdots\)
8325.2.a.z 8325.a 1.a $1$ $66.475$ \(\Q\) None 333.2.a.a \(1\) \(0\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+4q^{7}-3q^{8}-4q^{11}+\cdots\)
8325.2.a.ba 8325.a 1.a $1$ $66.475$ \(\Q\) None 1665.2.a.a \(2\) \(0\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-4q^{7}-q^{13}-8q^{14}+\cdots\)
8325.2.a.bb 8325.a 1.a $1$ $66.475$ \(\Q\) None 8325.2.a.b \(2\) \(0\) \(0\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{7}+6q^{11}-7q^{13}+\cdots\)
8325.2.a.bc 8325.a 1.a $1$ $66.475$ \(\Q\) None 555.2.c.a \(2\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+2q^{11}-q^{13}-4q^{16}+\cdots\)
8325.2.a.bd 8325.a 1.a $1$ $66.475$ \(\Q\) None 8325.2.a.b \(2\) \(0\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{7}-6q^{11}+7q^{13}+\cdots\)
8325.2.a.be 8325.a 1.a $1$ $66.475$ \(\Q\) None 2775.2.a.b \(2\) \(0\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{7}-5q^{13}+2q^{14}+\cdots\)
8325.2.a.bf 8325.a 1.a $2$ $66.475$ \(\Q(\sqrt{5}) \) None 555.2.a.c \(-3\) \(0\) \(0\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+3\beta q^{4}+(3-2\beta )q^{7}+\cdots\)
8325.2.a.bg 8325.a 1.a $2$ $66.475$ \(\Q(\sqrt{2}) \) None 2775.2.a.k \(-2\) \(0\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2q^{7}+\cdots\)
8325.2.a.bh 8325.a 1.a $2$ $66.475$ \(\Q(\sqrt{5}) \) None 555.2.a.e \(-1\) \(0\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+q^{7}+(-1+2\beta )q^{8}+\cdots\)
8325.2.a.bi 8325.a 1.a $2$ $66.475$ \(\Q(\sqrt{13}) \) None 555.2.a.d \(-1\) \(0\) \(0\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+3q^{7}-3q^{8}+(-1+\cdots)q^{11}+\cdots\)
8325.2.a.bj 8325.a 1.a $2$ $66.475$ \(\Q(\sqrt{7}) \) None 8325.2.a.bj \(0\) \(0\) \(0\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+5q^{4}-2q^{7}+3\beta q^{8}-2q^{13}+\cdots\)
8325.2.a.bk 8325.a 1.a $2$ $66.475$ \(\Q(\sqrt{7}) \) None 8325.2.a.bj \(0\) \(0\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+5q^{4}+2q^{7}+3\beta q^{8}+2q^{13}+\cdots\)
8325.2.a.bl 8325.a 1.a $2$ $66.475$ \(\Q(\sqrt{5}) \) None 555.2.a.f \(1\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots\)
8325.2.a.bm 8325.a 1.a $2$ $66.475$ \(\Q(\sqrt{13}) \) None 555.2.a.g \(1\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}-q^{7}+3q^{8}+(-1+\cdots)q^{11}+\cdots\)
8325.2.a.bn 8325.a 1.a $2$ $66.475$ \(\Q(\sqrt{2}) \) None 2775.2.a.k \(2\) \(0\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-2q^{7}+(3+\cdots)q^{8}+\cdots\)
8325.2.a.bo 8325.a 1.a $3$ $66.475$ 3.3.257.1 None 2775.2.a.u \(0\) \(0\) \(0\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-2+\beta _{2})q^{7}+\cdots\)
8325.2.a.bp 8325.a 1.a $3$ $66.475$ 3.3.257.1 None 2775.2.a.u \(0\) \(0\) \(0\) \(6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(2-\beta _{2})q^{7}+\cdots\)
8325.2.a.bq 8325.a 1.a $3$ $66.475$ 3.3.469.1 None 555.2.a.h \(1\) \(0\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
8325.2.a.br 8325.a 1.a $3$ $66.475$ 3.3.229.1 None 555.2.a.i \(2\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(2+\beta _{1})q^{4}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
8325.2.a.bs 8325.a 1.a $3$ $66.475$ 3.3.148.1 None 111.2.a.a \(3\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{7}+\cdots\)
8325.2.a.bt 8325.a 1.a $4$ $66.475$ 4.4.4400.1 None 555.2.c.b \(-2\) \(0\) \(0\) \(-8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-2-\beta _{3})q^{7}+\cdots\)
8325.2.a.bu 8325.a 1.a $4$ $66.475$ 4.4.27648.1 None 333.2.a.f \(0\) \(0\) \(0\) \(-8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-2q^{7}+(\beta _{1}+\beta _{3})q^{8}+\cdots\)
8325.2.a.bv 8325.a 1.a $4$ $66.475$ 4.4.6224.1 None 111.2.a.b \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-2+2\beta _{3})q^{7}+\cdots\)
8325.2.a.bw 8325.a 1.a $4$ $66.475$ 4.4.4400.1 None 555.2.c.b \(2\) \(0\) \(0\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(2-\beta _{3})q^{7}+\cdots\)
8325.2.a.bx 8325.a 1.a $5$ $66.475$ 5.5.600268.1 None 555.2.a.j \(-3\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}+(2-\beta _{3}+\beta _{4})q^{4}+\cdots\)
8325.2.a.by 8325.a 1.a $5$ $66.475$ 5.5.457904.1 None 1665.2.a.o \(-2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{2}-\beta _{4})q^{7}+\cdots\)
8325.2.a.bz 8325.a 1.a $5$ $66.475$ 5.5.176684.1 None 2775.2.a.ba \(-2\) \(0\) \(0\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{4})q^{4}+(1-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
8325.2.a.ca 8325.a 1.a $5$ $66.475$ 5.5.528933.1 None 2775.2.a.z \(-2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(2-\beta _{2}+\beta _{4})q^{4}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
8325.2.a.cb 8325.a 1.a $5$ $66.475$ 5.5.65657.1 None 925.2.a.g \(-1\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+\beta _{1}q^{4}+(-\beta _{2}-\beta _{3}-\beta _{4})q^{7}+\cdots\)
8325.2.a.cc 8325.a 1.a $5$ $66.475$ 5.5.368464.1 None 185.2.a.d \(0\) \(0\) \(0\) \(-7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(2-\beta _{1}-\beta _{4})q^{4}+(-1-\beta _{4})q^{7}+\cdots\)
8325.2.a.cd 8325.a 1.a $5$ $66.475$ 5.5.65657.1 None 925.2.a.g \(1\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+\beta _{1}q^{4}+(\beta _{2}+\beta _{3}+\beta _{4})q^{7}+\cdots\)
8325.2.a.ce 8325.a 1.a $5$ $66.475$ 5.5.176684.1 None 2775.2.a.ba \(2\) \(0\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(\beta _{2}-\beta _{4})q^{4}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
8325.2.a.cf 8325.a 1.a $5$ $66.475$ 5.5.457904.1 None 1665.2.a.o \(2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{2}-\beta _{4})q^{7}+\cdots\)
8325.2.a.cg 8325.a 1.a $5$ $66.475$ 5.5.528933.1 None 2775.2.a.z \(2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(2-\beta _{2}+\beta _{4})q^{4}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
8325.2.a.ch 8325.a 1.a $5$ $66.475$ 5.5.973904.1 None 185.2.a.e \(2\) \(0\) \(0\) \(-11\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+(2+\beta _{3})q^{4}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
8325.2.a.ci 8325.a 1.a $6$ $66.475$ 6.6.297869800.1 None 2775.2.a.be \(-4\) \(0\) \(0\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{7}+\cdots\)
8325.2.a.cj 8325.a 1.a $6$ $66.475$ 6.6.95034688.1 None 1665.2.a.t \(-2\) \(0\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
8325.2.a.ck 8325.a 1.a $6$ $66.475$ 6.6.95034688.1 None 1665.2.a.t \(2\) \(0\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
8325.2.a.cl 8325.a 1.a $6$ $66.475$ 6.6.297869800.1 None 2775.2.a.be \(4\) \(0\) \(0\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{7}+\cdots\)
8325.2.a.cm 8325.a 1.a $7$ $66.475$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 925.2.a.j \(-1\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{6}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
8325.2.a.cn 8325.a 1.a $7$ $66.475$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 925.2.a.j \(1\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{6}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
8325.2.a.co 8325.a 1.a $8$ $66.475$ 8.8.\(\cdots\).1 None 8325.2.a.co \(0\) \(0\) \(0\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(1-\beta _{1})q^{4}+(-1-\beta _{4})q^{7}+\cdots\)
8325.2.a.cp 8325.a 1.a $8$ $66.475$ 8.8.\(\cdots\).1 None 8325.2.a.co \(0\) \(0\) \(0\) \(6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(1-\beta _{1})q^{4}+(1+\beta _{4})q^{7}+\cdots\)
8325.2.a.cq 8325.a 1.a $9$ $66.475$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 185.2.b.a \(-5\) \(0\) \(0\) \(8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
8325.2.a.cr 8325.a 1.a $9$ $66.475$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 185.2.b.a \(5\) \(0\) \(0\) \(-8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
8325.2.a.cs 8325.a 1.a $10$ $66.475$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 8325.2.a.cs \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{2}-\beta _{7}+\cdots)q^{7}+\cdots\)
8325.2.a.ct 8325.a 1.a $10$ $66.475$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 8325.2.a.cs \(0\) \(0\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{2}+\beta _{7}+\cdots)q^{7}+\cdots\)
8325.2.a.cu 8325.a 1.a $13$ $66.475$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 555.2.c.c \(0\) \(0\) \(0\) \(-8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{9})q^{7}+\cdots\)
8325.2.a.cv 8325.a 1.a $13$ $66.475$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 555.2.c.c \(0\) \(0\) \(0\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{9})q^{7}+\cdots\)
8325.2.a.cw 8325.a 1.a $16$ $66.475$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 1665.2.c.g \(0\) \(0\) \(0\) \(-20\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{8})q^{7}+\cdots\)
8325.2.a.cx 8325.a 1.a $16$ $66.475$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 1665.2.c.g \(0\) \(0\) \(0\) \(20\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{8})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8325))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8325)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(333))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(555))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(925))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1665))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2775))\)\(^{\oplus 2}\)