Properties

Label 975.2.c
Level $975$
Weight $2$
Character orbit 975.c
Rep. character $\chi_{975}(274,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $11$
Sturm bound $280$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 975.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(280\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(975, [\chi])\).

Total New Old
Modular forms 152 36 116
Cusp forms 128 36 92
Eisenstein series 24 0 24

Trace form

\( 36 q - 44 q^{4} + 4 q^{6} - 36 q^{9} + O(q^{10}) \) \( 36 q - 44 q^{4} + 4 q^{6} - 36 q^{9} - 8 q^{11} + 24 q^{14} + 52 q^{16} - 8 q^{21} - 12 q^{24} - 8 q^{29} + 32 q^{34} + 44 q^{36} + 8 q^{39} + 16 q^{41} + 112 q^{44} - 40 q^{46} - 28 q^{49} + 24 q^{51} - 4 q^{54} - 72 q^{56} + 16 q^{59} + 16 q^{61} - 76 q^{64} + 40 q^{66} - 40 q^{69} + 16 q^{71} + 80 q^{74} + 32 q^{76} - 24 q^{79} + 36 q^{81} + 8 q^{84} - 40 q^{86} - 8 q^{89} - 8 q^{91} + 8 q^{94} - 12 q^{96} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(975, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
975.2.c.a 975.c 5.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None 195.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}+3iq^{7}+\cdots\)
975.2.c.b 975.c 5.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None 195.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}-3iq^{7}+\cdots\)
975.2.c.c 975.c 5.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None 195.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}-iq^{7}+\cdots\)
975.2.c.d 975.c 5.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None 975.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}-q^{6}+iq^{7}+3iq^{8}+\cdots\)
975.2.c.e 975.c 5.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None 195.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}-q^{6}+3iq^{8}+\cdots\)
975.2.c.f 975.c 5.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None 39.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}-q^{6}-4iq^{7}+\cdots\)
975.2.c.g 975.c 5.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None 975.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}+q^{4}+q^{6}-3iq^{7}+\cdots\)
975.2.c.h 975.c 5.b $4$ $7.785$ \(\Q(\zeta_{8})\) None 39.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
975.2.c.i 975.c 5.b $6$ $7.785$ 6.0.399424.1 None 195.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{2}q^{3}+(-3+\beta _{4})q^{4}+\beta _{1}q^{6}+\cdots\)
975.2.c.j 975.c 5.b $6$ $7.785$ 6.0.5089536.1 None 975.2.a.n \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+\beta _{4}q^{3}+(-2+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots\)
975.2.c.k 975.c 5.b $6$ $7.785$ 6.0.350464.1 None 975.2.a.m \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(975, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(975, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)