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Properties

Label 1925.2.a
Level $1925$
Weight $2$
Character orbit 1925.a
Rep. character $\chi_{1925}(1,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $32$
Sturm bound $480$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1925.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 32 \)
Sturm bound: \(480\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(2\), \(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1925))\).

Total New Old
Modular forms 252 96 156
Cusp forms 229 96 133
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.

\(5\)\(7\)\(11\)FrickeDim
\(+\)\(+\)\(+\)$+$\(9\)
\(+\)\(+\)\(-\)$-$\(13\)
\(+\)\(-\)\(+\)$-$\(15\)
\(+\)\(-\)\(-\)$+$\(7\)
\(-\)\(+\)\(+\)$-$\(13\)
\(-\)\(+\)\(-\)$+$\(13\)
\(-\)\(-\)\(+\)$+$\(9\)
\(-\)\(-\)\(-\)$-$\(17\)
Plus space\(+\)\(38\)
Minus space\(-\)\(58\)

Trace form

\( 96 q + 2 q^{2} + 2 q^{3} + 106 q^{4} - 4 q^{6} - 6 q^{8} + 102 q^{9} + O(q^{10}) \) \( 96 q + 2 q^{2} + 2 q^{3} + 106 q^{4} - 4 q^{6} - 6 q^{8} + 102 q^{9} + 4 q^{11} - 4 q^{12} + 16 q^{13} + 4 q^{14} + 126 q^{16} + 12 q^{17} + 34 q^{18} + 12 q^{19} - 2 q^{22} - 6 q^{23} + 28 q^{24} - 44 q^{26} - 10 q^{27} - 24 q^{29} + 18 q^{31} + 10 q^{32} + 2 q^{33} + 20 q^{34} + 158 q^{36} + 30 q^{37} + 16 q^{38} - 12 q^{41} + 16 q^{42} - 8 q^{43} + 10 q^{44} + 24 q^{46} + 16 q^{47} + 64 q^{48} + 96 q^{49} + 36 q^{51} + 8 q^{52} + 24 q^{54} + 12 q^{56} + 12 q^{57} - 28 q^{58} - 10 q^{59} + 36 q^{61} - 76 q^{62} + 142 q^{64} - 26 q^{67} + 48 q^{68} + 6 q^{69} - 18 q^{71} + 42 q^{72} + 36 q^{73} - 20 q^{74} + 88 q^{76} - 4 q^{77} - 16 q^{78} + 28 q^{79} + 96 q^{81} - 20 q^{82} - 32 q^{83} - 28 q^{84} + 80 q^{86} + 52 q^{87} + 6 q^{88} - 50 q^{89} - 36 q^{92} - 50 q^{93} - 148 q^{94} - 68 q^{96} + 26 q^{97} + 2 q^{98} - 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1925))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 7 11
1925.2.a.a 1925.a 1.a $1$ $15.371$ \(\Q\) None \(-2\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{7}-3q^{9}+q^{11}+\cdots\)
1925.2.a.b 1925.a 1.a $1$ $15.371$ \(\Q\) None \(-1\) \(-2\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}+2q^{6}-q^{7}+3q^{8}+\cdots\)
1925.2.a.c 1925.a 1.a $1$ $15.371$ \(\Q\) None \(-1\) \(-2\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}+2q^{6}+q^{7}+3q^{8}+\cdots\)
1925.2.a.d 1925.a 1.a $1$ $15.371$ \(\Q\) None \(-1\) \(-2\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}+2q^{6}+q^{7}+3q^{8}+\cdots\)
1925.2.a.e 1925.a 1.a $1$ $15.371$ \(\Q\) None \(0\) \(-2\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{4}+q^{7}+q^{9}-q^{11}+4q^{12}+\cdots\)
1925.2.a.f 1925.a 1.a $1$ $15.371$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{7}-2q^{9}-q^{11}+2q^{12}+\cdots\)
1925.2.a.g 1925.a 1.a $1$ $15.371$ \(\Q\) None \(0\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}-q^{7}+q^{9}-q^{11}-4q^{12}+\cdots\)
1925.2.a.h 1925.a 1.a $1$ $15.371$ \(\Q\) None \(0\) \(3\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-2q^{4}+q^{7}+6q^{9}-q^{11}+\cdots\)
1925.2.a.i 1925.a 1.a $1$ $15.371$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{7}-3q^{8}-3q^{9}+q^{11}+\cdots\)
1925.2.a.j 1925.a 1.a $1$ $15.371$ \(\Q\) None \(1\) \(2\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}-q^{4}+2q^{6}-q^{7}-3q^{8}+\cdots\)
1925.2.a.k 1925.a 1.a $1$ $15.371$ \(\Q\) None \(1\) \(2\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}-q^{4}+2q^{6}-q^{7}-3q^{8}+\cdots\)
1925.2.a.l 1925.a 1.a $1$ $15.371$ \(\Q\) None \(1\) \(2\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}-q^{4}+2q^{6}+q^{7}-3q^{8}+\cdots\)
1925.2.a.m 1925.a 1.a $1$ $15.371$ \(\Q\) None \(2\) \(0\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{7}-3q^{9}+q^{11}+\cdots\)
1925.2.a.n 1925.a 1.a $2$ $15.371$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
1925.2.a.o 1925.a 1.a $2$ $15.371$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
1925.2.a.p 1925.a 1.a $2$ $15.371$ \(\Q(\sqrt{13}) \) None \(-1\) \(2\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(1+\beta )q^{4}-\beta q^{6}+q^{7}+\cdots\)
1925.2.a.q 1925.a 1.a $2$ $15.371$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}+(3-\beta )q^{6}+\cdots\)
1925.2.a.r 1925.a 1.a $2$ $15.371$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{3}+3q^{4}+(-5+\cdots)q^{6}+\cdots\)
1925.2.a.s 1925.a 1.a $2$ $15.371$ \(\Q(\sqrt{13}) \) None \(1\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(1+\beta )q^{4}-\beta q^{6}-q^{7}+\cdots\)
1925.2.a.t 1925.a 1.a $2$ $15.371$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1-2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
1925.2.a.u 1925.a 1.a $3$ $15.371$ 3.3.148.1 None \(-1\) \(0\) \(0\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1925.2.a.v 1925.a 1.a $3$ $15.371$ 3.3.148.1 None \(3\) \(2\) \(0\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(1-\beta _{1})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
1925.2.a.w 1925.a 1.a $3$ $15.371$ 3.3.148.1 None \(3\) \(4\) \(0\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(1+\beta _{1})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
1925.2.a.x 1925.a 1.a $4$ $15.371$ 4.4.11348.1 None \(-2\) \(-2\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(-1-\beta _{3})q^{3}+(2+\cdots)q^{4}+\cdots\)
1925.2.a.y 1925.a 1.a $6$ $15.371$ 6.6.9921856.1 None \(0\) \(-6\) \(0\) \(6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-\beta _{2}-\beta _{4}-\beta _{5})q^{3}+\beta _{2}q^{4}+\cdots\)
1925.2.a.z 1925.a 1.a $6$ $15.371$ 6.6.9921856.1 None \(0\) \(6\) \(0\) \(-6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{4}+\beta _{5})q^{3}+\beta _{2}q^{4}+\cdots\)
1925.2.a.ba 1925.a 1.a $7$ $15.371$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(0\) \(0\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(2-\beta _{2}+\beta _{3})q^{4}+\cdots\)
1925.2.a.bb 1925.a 1.a $7$ $15.371$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(0\) \(0\) \(-7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{6}+\cdots\)
1925.2.a.bc 1925.a 1.a $7$ $15.371$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(1\) \(0\) \(0\) \(7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(2-\beta _{2}+\beta _{3})q^{4}+\cdots\)
1925.2.a.bd 1925.a 1.a $7$ $15.371$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(1\) \(0\) \(0\) \(7\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{6}+\cdots\)
1925.2.a.be 1925.a 1.a $8$ $15.371$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(-6\) \(0\) \(-8\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{5})q^{3}+(2+\cdots)q^{4}+\cdots\)
1925.2.a.bf 1925.a 1.a $8$ $15.371$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(6\) \(0\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{5})q^{3}+(2+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1925))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1925)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 2}\)