Properties

Label 2325.2.a
Level $2325$
Weight $2$
Character orbit 2325.a
Rep. character $\chi_{2325}(1,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $30$
Sturm bound $640$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2325 = 3 \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2325.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 30 \)
Sturm bound: \(640\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2325))\).

Total New Old
Modular forms 332 96 236
Cusp forms 309 96 213
Eisenstein series 23 0 23

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

\(3\)\(5\)\(31\)FrickeDim
\(+\)\(+\)\(+\)$+$\(11\)
\(+\)\(+\)\(-\)$-$\(11\)
\(+\)\(-\)\(+\)$-$\(11\)
\(+\)\(-\)\(-\)$+$\(15\)
\(-\)\(+\)\(+\)$-$\(14\)
\(-\)\(+\)\(-\)$+$\(8\)
\(-\)\(-\)\(+\)$+$\(9\)
\(-\)\(-\)\(-\)$-$\(17\)
Plus space\(+\)\(43\)
Minus space\(-\)\(53\)

Trace form

\( 96 q - 2 q^{2} + 94 q^{4} + 96 q^{9} + O(q^{10}) \) \( 96 q - 2 q^{2} + 94 q^{4} + 96 q^{9} + 4 q^{11} + 8 q^{12} + 12 q^{13} + 10 q^{14} + 98 q^{16} + 16 q^{17} - 2 q^{18} + 16 q^{19} - 12 q^{22} + 4 q^{23} - 12 q^{24} - 40 q^{26} - 6 q^{28} - 44 q^{29} + 6 q^{31} - 22 q^{32} - 32 q^{34} + 94 q^{36} - 20 q^{37} - 14 q^{38} + 8 q^{39} + 4 q^{41} + 12 q^{43} - 32 q^{44} - 64 q^{46} + 16 q^{48} + 124 q^{49} + 16 q^{51} + 36 q^{52} + 8 q^{53} - 44 q^{56} + 8 q^{57} + 28 q^{58} + 16 q^{59} + 92 q^{64} + 24 q^{66} + 24 q^{67} + 16 q^{68} + 8 q^{69} - 16 q^{71} + 44 q^{73} - 12 q^{74} + 90 q^{76} - 4 q^{77} + 24 q^{78} + 96 q^{81} + 50 q^{82} - 32 q^{83} + 40 q^{84} - 12 q^{86} - 8 q^{87} - 44 q^{88} + 24 q^{89} + 4 q^{91} + 12 q^{92} - 2 q^{93} + 80 q^{94} - 4 q^{96} - 4 q^{97} + 28 q^{98} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2325))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 31
2325.2.a.a 2325.a 1.a $1$ $18.565$ \(\Q\) None \(-2\) \(-1\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+4q^{7}+\cdots\)
2325.2.a.b 2325.a 1.a $1$ $18.565$ \(\Q\) None \(-2\) \(1\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-4q^{7}+\cdots\)
2325.2.a.c 2325.a 1.a $1$ $18.565$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}-2q^{7}+3q^{8}+\cdots\)
2325.2.a.d 2325.a 1.a $1$ $18.565$ \(\Q\) None \(-1\) \(1\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+2q^{7}+3q^{8}+\cdots\)
2325.2.a.e 2325.a 1.a $1$ $18.565$ \(\Q\) None \(-1\) \(1\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+2q^{7}+3q^{8}+\cdots\)
2325.2.a.f 2325.a 1.a $1$ $18.565$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{9}-3q^{11}+2q^{12}+\cdots\)
2325.2.a.g 2325.a 1.a $1$ $18.565$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{9}-3q^{11}-2q^{12}+\cdots\)
2325.2.a.h 2325.a 1.a $1$ $18.565$ \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-2q^{7}-3q^{8}+\cdots\)
2325.2.a.i 2325.a 1.a $1$ $18.565$ \(\Q\) None \(1\) \(-1\) \(0\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+4q^{7}-3q^{8}+\cdots\)
2325.2.a.j 2325.a 1.a $1$ $18.565$ \(\Q\) None \(1\) \(1\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}+2q^{7}-3q^{8}+\cdots\)
2325.2.a.k 2325.a 1.a $1$ $18.565$ \(\Q\) None \(2\) \(-1\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+4q^{7}+\cdots\)
2325.2.a.l 2325.a 1.a $1$ $18.565$ \(\Q\) None \(2\) \(1\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}-4q^{7}+\cdots\)
2325.2.a.m 2325.a 1.a $2$ $18.565$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}+(3-\beta )q^{7}+\cdots\)
2325.2.a.n 2325.a 1.a $2$ $18.565$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
2325.2.a.o 2325.a 1.a $2$ $18.565$ \(\Q(\sqrt{5}) \) None \(3\) \(2\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots\)
2325.2.a.p 2325.a 1.a $3$ $18.565$ 3.3.148.1 None \(-3\) \(-3\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2325.2.a.q 2325.a 1.a $3$ $18.565$ 3.3.148.1 None \(-1\) \(-3\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
2325.2.a.r 2325.a 1.a $3$ $18.565$ 3.3.564.1 None \(-1\) \(3\) \(0\) \(-8\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
2325.2.a.s 2325.a 1.a $3$ $18.565$ 3.3.229.1 None \(0\) \(-3\) \(0\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
2325.2.a.t 2325.a 1.a $3$ $18.565$ 3.3.148.1 None \(0\) \(-3\) \(0\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
2325.2.a.u 2325.a 1.a $3$ $18.565$ 3.3.148.1 None \(0\) \(3\) \(0\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
2325.2.a.v 2325.a 1.a $4$ $18.565$ 4.4.8468.1 None \(-2\) \(4\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+q^{3}+(2-\beta _{1})q^{4}+\beta _{2}q^{6}+\cdots\)
2325.2.a.w 2325.a 1.a $5$ $18.565$ 5.5.126032.1 None \(-3\) \(5\) \(0\) \(-8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{2}+q^{3}+(1-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
2325.2.a.x 2325.a 1.a $5$ $18.565$ 5.5.126032.1 None \(3\) \(-5\) \(0\) \(8\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{3})q^{2}-q^{3}+(1-\beta _{1}+\beta _{3})q^{4}+\cdots\)
2325.2.a.y 2325.a 1.a $6$ $18.565$ 6.6.75968016.1 None \(-1\) \(-6\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+\beta _{1}q^{6}+\cdots\)
2325.2.a.z 2325.a 1.a $6$ $18.565$ 6.6.136751504.1 None \(-1\) \(6\) \(0\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
2325.2.a.ba 2325.a 1.a $6$ $18.565$ 6.6.136751504.1 None \(1\) \(-6\) \(0\) \(-6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
2325.2.a.bb 2325.a 1.a $6$ $18.565$ 6.6.75968016.1 None \(1\) \(6\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{4}+\beta _{5})q^{4}+\beta _{1}q^{6}+\cdots\)
2325.2.a.bc 2325.a 1.a $11$ $18.565$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-3\) \(-11\) \(0\) \(-8\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
2325.2.a.bd 2325.a 1.a $11$ $18.565$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(3\) \(11\) \(0\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2325))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2325)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(465))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(775))\)\(^{\oplus 2}\)