Properties

Label 1925.2.b
Level $1925$
Weight $2$
Character orbit 1925.b
Rep. character $\chi_{1925}(1849,\cdot)$
Character field $\Q$
Dimension $88$
Newform subspaces $18$
Sturm bound $480$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1925.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(480\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(3\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1925, [\chi])\).

Total New Old
Modular forms 252 88 164
Cusp forms 228 88 140
Eisenstein series 24 0 24

Trace form

\( 88 q - 100 q^{4} + 16 q^{6} - 76 q^{9} + O(q^{10}) \) \( 88 q - 100 q^{4} + 16 q^{6} - 76 q^{9} - 8 q^{11} + 8 q^{14} + 124 q^{16} - 32 q^{19} + 8 q^{24} - 24 q^{26} + 40 q^{29} + 20 q^{31} - 40 q^{34} + 68 q^{36} - 16 q^{39} - 16 q^{41} + 20 q^{44} + 80 q^{46} - 88 q^{49} + 24 q^{51} + 40 q^{54} - 24 q^{56} - 44 q^{59} - 196 q^{64} - 36 q^{69} - 44 q^{71} + 208 q^{76} - 24 q^{79} + 8 q^{81} - 40 q^{86} + 108 q^{89} - 16 q^{91} - 16 q^{94} - 80 q^{96} + 44 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1925, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1925.2.b.a 1925.b 5.b $2$ $15.371$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{4}-iq^{7}+3q^{9}+q^{11}+\cdots\)
1925.2.b.b 1925.b 5.b $2$ $15.371$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+iq^{7}+3iq^{8}+3q^{9}+\cdots\)
1925.2.b.c 1925.b 5.b $2$ $15.371$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2iq^{3}+q^{4}+2q^{6}-iq^{7}+\cdots\)
1925.2.b.d 1925.b 5.b $2$ $15.371$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2iq^{3}+q^{4}+2q^{6}-iq^{7}+\cdots\)
1925.2.b.e 1925.b 5.b $2$ $15.371$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+2q^{4}-iq^{7}-6q^{9}-q^{11}+\cdots\)
1925.2.b.f 1925.b 5.b $2$ $15.371$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+2q^{4}+iq^{7}-q^{9}-q^{11}+\cdots\)
1925.2.b.g 1925.b 5.b $2$ $15.371$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2q^{4}+iq^{7}+2q^{9}-q^{11}+\cdots\)
1925.2.b.h 1925.b 5.b $4$ $15.371$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-3q^{4}+(-5+\cdots)q^{6}+\cdots\)
1925.2.b.i 1925.b 5.b $4$ $15.371$ \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1925.2.b.j 1925.b 5.b $4$ $15.371$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}^{2}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1925.2.b.k 1925.b 5.b $4$ $15.371$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
1925.2.b.l 1925.b 5.b $4$ $15.371$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1925.2.b.m 1925.b 5.b $6$ $15.371$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)
1925.2.b.n 1925.b 5.b $6$ $15.371$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}+\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)
1925.2.b.o 1925.b 5.b $6$ $15.371$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-\beta _{5}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1925.2.b.p 1925.b 5.b $8$ $15.371$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{4}-\beta _{6})q^{2}-\beta _{7}q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
1925.2.b.q 1925.b 5.b $14$ $15.371$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-2-\beta _{7}+\beta _{8}+\cdots)q^{4}+\cdots\)
1925.2.b.r 1925.b 5.b $14$ $15.371$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(-2+\beta _{2})q^{4}-\beta _{10}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1925, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1925, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)