Properties

Label 2925.2.c
Level $2925$
Weight $2$
Character orbit 2925.c
Rep. character $\chi_{2925}(2224,\cdot)$
Character field $\Q$
Dimension $90$
Newform subspaces $26$
Sturm bound $840$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2925.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(840\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2925, [\chi])\).

Total New Old
Modular forms 444 90 354
Cusp forms 396 90 306
Eisenstein series 48 0 48

Trace form

\( 90 q - 98 q^{4} + O(q^{10}) \) \( 90 q - 98 q^{4} - 4 q^{11} - 20 q^{14} + 106 q^{16} - 24 q^{19} - 6 q^{26} - 20 q^{29} + 24 q^{31} + 32 q^{34} - 16 q^{41} - 36 q^{44} - 28 q^{46} - 46 q^{49} + 116 q^{56} + 32 q^{59} + 4 q^{61} - 178 q^{64} - 68 q^{71} - 84 q^{74} + 104 q^{76} - 12 q^{79} - 44 q^{86} - 8 q^{89} + 16 q^{91} - 28 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2925, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2925.2.c.a 2925.c 5.b $2$ $23.356$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{4}+iq^{7}-5q^{11}-iq^{13}+\cdots\)
2925.2.c.b 2925.c 5.b $2$ $23.356$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{4}-2iq^{7}-2q^{11}-iq^{13}+\cdots\)
2925.2.c.c 2925.c 5.b $2$ $23.356$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{4}-3iq^{7}+q^{11}-iq^{13}+\cdots\)
2925.2.c.d 2925.c 5.b $2$ $23.356$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{4}+3iq^{7}+5q^{11}+iq^{13}+\cdots\)
2925.2.c.e 2925.c 5.b $2$ $23.356$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+4iq^{7}+3iq^{8}-4q^{11}+\cdots\)
2925.2.c.f 2925.c 5.b $2$ $23.356$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+3iq^{8}-4q^{11}-iq^{13}+\cdots\)
2925.2.c.g 2925.c 5.b $2$ $23.356$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}-2iq^{7}+3iq^{8}-4q^{11}+\cdots\)
2925.2.c.h 2925.c 5.b $2$ $23.356$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}-4iq^{7}+3iq^{8}-2q^{11}+\cdots\)
2925.2.c.i 2925.c 5.b $2$ $23.356$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+3iq^{7}+3iq^{8}+q^{11}+\cdots\)
2925.2.c.j 2925.c 5.b $2$ $23.356$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}-iq^{7}+3iq^{8}+q^{11}+\cdots\)
2925.2.c.k 2925.c 5.b $2$ $23.356$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+2iq^{7}+3iq^{8}+4q^{11}+\cdots\)
2925.2.c.l 2925.c 5.b $2$ $23.356$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}-iq^{7}-3q^{11}-iq^{13}+4q^{16}+\cdots\)
2925.2.c.m 2925.c 5.b $2$ $23.356$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}-iq^{7}+3q^{11}-iq^{13}+4q^{16}+\cdots\)
2925.2.c.n 2925.c 5.b $2$ $23.356$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}-4iq^{7}+6q^{11}-iq^{13}+4q^{16}+\cdots\)
2925.2.c.o 2925.c 5.b $4$ $23.356$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}+(-\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots\)
2925.2.c.p 2925.c 5.b $4$ $23.356$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
2925.2.c.q 2925.c 5.b $4$ $23.356$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
2925.2.c.r 2925.c 5.b $4$ $23.356$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
2925.2.c.s 2925.c 5.b $4$ $23.356$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{2}-q^{4}+2\zeta_{12}q^{7}+\zeta_{12}^{2}q^{8}+\cdots\)
2925.2.c.t 2925.c 5.b $4$ $23.356$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{2}-q^{4}+\zeta_{12}q^{7}-\zeta_{12}^{2}q^{8}+\cdots\)
2925.2.c.u 2925.c 5.b $4$ $23.356$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
2925.2.c.v 2925.c 5.b $4$ $23.356$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{2}-q^{4}-2\zeta_{12}q^{7}+\zeta_{12}^{2}q^{8}+\cdots\)
2925.2.c.w 2925.c 5.b $6$ $23.356$ 6.0.399424.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(-3+\beta _{4})q^{4}-\beta _{5}q^{7}+(2\beta _{2}+\cdots)q^{8}+\cdots\)
2925.2.c.x 2925.c 5.b $6$ $23.356$ 6.0.5089536.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(-2+\beta _{3})q^{4}+(2\beta _{4}-\beta _{5})q^{7}+\cdots\)
2925.2.c.y 2925.c 5.b $6$ $23.356$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2})q^{4}+\cdots\)
2925.2.c.z 2925.c 5.b $12$ $23.356$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+(-2+\beta _{1})q^{4}+(\beta _{4}+\beta _{9}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2925, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2925, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)