Properties

Label 7600.2.a
Level $7600$
Weight $2$
Character orbit 7600.a
Rep. character $\chi_{7600}(1,\cdot)$
Character field $\Q$
Dimension $171$
Newform subspaces $66$
Sturm bound $2400$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7600.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 66 \)
Sturm bound: \(2400\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7600))\).

Total New Old
Modular forms 1236 171 1065
Cusp forms 1165 171 994
Eisenstein series 71 0 71

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

\(2\)\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(19\)
\(+\)\(+\)\(-\)\(-\)\(22\)
\(+\)\(-\)\(+\)\(-\)\(25\)
\(+\)\(-\)\(-\)\(+\)\(19\)
\(-\)\(+\)\(+\)\(-\)\(20\)
\(-\)\(+\)\(-\)\(+\)\(20\)
\(-\)\(-\)\(+\)\(+\)\(23\)
\(-\)\(-\)\(-\)\(-\)\(23\)
Plus space\(+\)\(81\)
Minus space\(-\)\(90\)

Trace form

\( 171 q - 2 q^{7} + 171 q^{9} + O(q^{10}) \) \( 171 q - 2 q^{7} + 171 q^{9} - 10 q^{11} + 2 q^{13} - 2 q^{17} - 3 q^{19} + 8 q^{21} - 16 q^{23} - 24 q^{27} + 18 q^{29} + 8 q^{33} + 18 q^{37} - 28 q^{39} - 2 q^{41} + 18 q^{43} - 10 q^{47} + 179 q^{49} - 44 q^{51} + 10 q^{53} + 16 q^{59} + 10 q^{61} - 30 q^{63} - 20 q^{67} - 8 q^{69} - 12 q^{71} - 2 q^{73} - 8 q^{77} - 8 q^{79} + 163 q^{81} - 8 q^{83} + 12 q^{87} - 18 q^{89} - 8 q^{91} + 8 q^{93} - 10 q^{97} - 10 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7600))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 19
7600.2.a.a 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(-3\) \(0\) \(-5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{7}+6q^{9}+4q^{11}+q^{13}+\cdots\)
7600.2.a.b 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(-2\) \(0\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-3q^{7}+q^{9}+3q^{11}+4q^{13}+\cdots\)
7600.2.a.c 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(-2\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots\)
7600.2.a.d 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(-2\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}+4q^{11}-4q^{13}+2q^{17}+\cdots\)
7600.2.a.e 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(-2\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{7}+q^{9}-4q^{11}-8q^{17}+\cdots\)
7600.2.a.f 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(-2\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
7600.2.a.g 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}-2q^{9}+3q^{13}+7q^{17}+\cdots\)
7600.2.a.h 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(-1\) \(0\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}-2q^{9}-2q^{11}+q^{13}+\cdots\)
7600.2.a.i 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}+4q^{11}-2q^{13}+4q^{17}+\cdots\)
7600.2.a.j 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}+4q^{11}+4q^{13}-6q^{17}+\cdots\)
7600.2.a.k 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{9}+4q^{11}+6q^{13}+6q^{17}+q^{19}+\cdots\)
7600.2.a.l 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}+4q^{11}+2q^{13}-4q^{17}+\cdots\)
7600.2.a.m 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}-2q^{9}+q^{13}+3q^{17}+\cdots\)
7600.2.a.n 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}-2q^{9}+6q^{11}-5q^{13}+\cdots\)
7600.2.a.o 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(1\) \(0\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{7}-2q^{9}-2q^{11}-q^{13}+\cdots\)
7600.2.a.p 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(2\) \(0\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-3q^{7}+q^{9}-5q^{11}+4q^{13}+\cdots\)
7600.2.a.q 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(2\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{7}+q^{9}-4q^{11}+8q^{17}+\cdots\)
7600.2.a.r 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(2\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots\)
7600.2.a.s 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(2\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{7}+q^{9}+4q^{11}-6q^{17}+\cdots\)
7600.2.a.t 7600.a 1.a $1$ $60.686$ \(\Q\) None \(0\) \(3\) \(0\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{7}+6q^{9}-4q^{11}-q^{13}+\cdots\)
7600.2.a.u 7600.a 1.a $2$ $60.686$ \(\Q(\sqrt{2}) \) None \(0\) \(-4\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{3}+(-2-2\beta )q^{7}+(3-4\beta )q^{9}+\cdots\)
7600.2.a.v 7600.a 1.a $2$ $60.686$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(-6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(-3-\beta )q^{7}-2\beta q^{9}+\cdots\)
7600.2.a.w 7600.a 1.a $2$ $60.686$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+2\beta q^{7}+(3+2\beta )q^{9}+\cdots\)
7600.2.a.x 7600.a 1.a $2$ $60.686$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(1-\beta )q^{7}-2\beta q^{9}+\cdots\)
7600.2.a.y 7600.a 1.a $2$ $60.686$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-\beta q^{7}+(1+\beta )q^{9}-4q^{11}+\cdots\)
7600.2.a.z 7600.a 1.a $2$ $60.686$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-2+2\beta )q^{7}-q^{9}+(-2+\cdots)q^{11}+\cdots\)
7600.2.a.ba 7600.a 1.a $2$ $60.686$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2\beta q^{7}-q^{9}+(-2-2\beta )q^{11}+\cdots\)
7600.2.a.bb 7600.a 1.a $2$ $60.686$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(2+2\beta )q^{7}-q^{9}+(-2-2\beta )q^{11}+\cdots\)
7600.2.a.bc 7600.a 1.a $2$ $60.686$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1-\beta )q^{7}+2\beta q^{9}+\cdots\)
7600.2.a.bd 7600.a 1.a $2$ $60.686$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(1+2\beta )q^{9}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
7600.2.a.be 7600.a 1.a $2$ $60.686$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-2\beta q^{7}+(3+2\beta )q^{9}+(1+\cdots)q^{13}+\cdots\)
7600.2.a.bf 7600.a 1.a $2$ $60.686$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+2q^{7}+(1+2\beta )q^{9}+2\beta q^{11}+\cdots\)
7600.2.a.bg 7600.a 1.a $2$ $60.686$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(3-\beta )q^{7}+2\beta q^{9}-\beta q^{11}+\cdots\)
7600.2.a.bh 7600.a 1.a $3$ $60.686$ 3.3.169.1 None \(0\) \(-2\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1-\beta _{1})q^{7}+(1+\cdots)q^{9}+\cdots\)
7600.2.a.bi 7600.a 1.a $3$ $60.686$ 3.3.568.1 None \(0\) \(-2\) \(0\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1-\beta _{1})q^{7}+(2+\cdots)q^{9}+\cdots\)
7600.2.a.bj 7600.a 1.a $3$ $60.686$ 3.3.257.1 None \(0\) \(-2\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1})q^{7}+(1+\cdots)q^{9}+\cdots\)
7600.2.a.bk 7600.a 1.a $3$ $60.686$ 3.3.993.1 None \(0\) \(-2\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
7600.2.a.bl 7600.a 1.a $3$ $60.686$ 3.3.321.1 None \(0\) \(-2\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2})q^{7}+\cdots\)
7600.2.a.bm 7600.a 1.a $3$ $60.686$ 3.3.257.1 None \(0\) \(-2\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2})q^{3}+(-1+\beta _{1}-2\beta _{2})q^{7}+\cdots\)
7600.2.a.bn 7600.a 1.a $3$ $60.686$ \(\Q(\zeta_{14})^+\) None \(0\) \(-2\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(1-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
7600.2.a.bo 7600.a 1.a $3$ $60.686$ 3.3.568.1 None \(0\) \(-1\) \(0\) \(-5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-2-\beta _{2})q^{7}+(1+2\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.bp 7600.a 1.a $3$ $60.686$ 3.3.316.1 None \(0\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+2\beta _{1}-\beta _{2})q^{7}+\beta _{2}q^{9}+\cdots\)
7600.2.a.bq 7600.a 1.a $3$ $60.686$ 3.3.229.1 None \(0\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+\beta _{1}q^{7}+(1-\beta _{1})q^{9}+(-2+\cdots)q^{13}+\cdots\)
7600.2.a.br 7600.a 1.a $3$ $60.686$ \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-\beta _{1}+2\beta _{2})q^{7}+(-1+\beta _{2})q^{9}+\cdots\)
7600.2.a.bs 7600.a 1.a $3$ $60.686$ \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}-2\beta _{2})q^{7}+(-1+\beta _{2})q^{9}+\cdots\)
7600.2.a.bt 7600.a 1.a $3$ $60.686$ 3.3.257.1 None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+\beta _{2}q^{7}+(\beta _{1}-\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
7600.2.a.bu 7600.a 1.a $3$ $60.686$ 3.3.257.1 None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-\beta _{2}q^{7}+(\beta _{1}-\beta _{2})q^{9}+(1+\cdots)q^{11}+\cdots\)
7600.2.a.bv 7600.a 1.a $3$ $60.686$ 3.3.961.1 None \(0\) \(1\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(2-\beta _{1}+\beta _{2})q^{7}+(5-\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.bw 7600.a 1.a $3$ $60.686$ \(\Q(\zeta_{14})^+\) None \(0\) \(2\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{1}+2\beta _{2})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.bx 7600.a 1.a $3$ $60.686$ 3.3.148.1 None \(0\) \(2\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(\beta _{1}-\beta _{2})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.by 7600.a 1.a $3$ $60.686$ 3.3.257.1 None \(0\) \(2\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{1})q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.bz 7600.a 1.a $3$ $60.686$ 3.3.993.1 None \(0\) \(2\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{2})q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.ca 7600.a 1.a $3$ $60.686$ 3.3.321.1 None \(0\) \(2\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(1-2\beta _{1}-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
7600.2.a.cb 7600.a 1.a $3$ $60.686$ 3.3.257.1 None \(0\) \(2\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}-\beta _{2})q^{3}+(1-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
7600.2.a.cc 7600.a 1.a $3$ $60.686$ 3.3.169.1 None \(0\) \(2\) \(0\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1+\beta _{1})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.cd 7600.a 1.a $3$ $60.686$ 3.3.568.1 None \(0\) \(2\) \(0\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1+\beta _{1})q^{7}+(2+\beta _{2})q^{9}+\cdots\)
7600.2.a.ce 7600.a 1.a $4$ $60.686$ \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
7600.2.a.cf 7600.a 1.a $4$ $60.686$ 4.4.11344.1 None \(0\) \(2\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(1-\beta _{1})q^{7}+(2-\beta _{3})q^{9}+\cdots\)
7600.2.a.cg 7600.a 1.a $6$ $60.686$ 6.6.253565184.1 None \(0\) \(-2\) \(0\) \(-6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.ch 7600.a 1.a $6$ $60.686$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-2\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{4})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.ci 7600.a 1.a $6$ $60.686$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
7600.2.a.cj 7600.a 1.a $6$ $60.686$ 6.6.56310016.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}-\beta _{4}q^{7}+(2-\beta _{1}+\beta _{5})q^{9}+\cdots\)
7600.2.a.ck 7600.a 1.a $6$ $60.686$ 6.6.66064384.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{3}+(-\beta _{2}-\beta _{5})q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)
7600.2.a.cl 7600.a 1.a $6$ $60.686$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(2\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{4})q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7600.2.a.cm 7600.a 1.a $6$ $60.686$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(2\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{3}q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
7600.2.a.cn 7600.a 1.a $6$ $60.686$ 6.6.253565184.1 None \(0\) \(2\) \(0\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{1}+\beta _{3})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(760))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(950))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1900))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3800))\)\(^{\oplus 2}\)