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Properties

Label 975.2.b
Level $975$
Weight $2$
Character orbit 975.b
Rep. character $\chi_{975}(376,\cdot)$
Character field $\Q$
Dimension $46$
Newform subspaces $12$
Sturm bound $280$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 975.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(280\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\), \(17\)

Dimensions

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

Total New Old
Modular forms 152 46 106
Cusp forms 128 46 82
Eisenstein series 24 0 24

Trace form

\( 46 q - 2 q^{3} - 50 q^{4} + 46 q^{9} + O(q^{10}) \) \( 46 q - 2 q^{3} - 50 q^{4} + 46 q^{9} + 10 q^{12} - 2 q^{13} - 4 q^{14} + 70 q^{16} + 12 q^{17} - 36 q^{22} + 8 q^{23} + 20 q^{26} - 2 q^{27} + 36 q^{29} - 50 q^{36} - 12 q^{38} + 12 q^{39} + 28 q^{42} + 24 q^{43} - 6 q^{48} - 10 q^{49} + 4 q^{51} - 6 q^{52} + 4 q^{53} - 76 q^{56} - 40 q^{61} - 4 q^{62} - 74 q^{64} - 20 q^{66} - 36 q^{68} - 32 q^{74} - 32 q^{77} + 4 q^{78} - 8 q^{79} + 46 q^{81} - 40 q^{82} - 4 q^{87} + 68 q^{88} - 6 q^{91} + 80 q^{92} - 20 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
975.2.b.a 975.b 13.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-q^{3}-2q^{4}-2iq^{6}-3iq^{7}+\cdots\)
975.2.b.b 975.b 13.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{3}+q^{4}-iq^{6}-2iq^{7}+\cdots\)
975.2.b.c 975.b 13.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+q^{3}-2q^{4}+2iq^{6}-3iq^{7}+\cdots\)
975.2.b.d 975.b 13.b $2$ $7.785$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}+q^{3}-q^{4}-\zeta_{6}q^{6}+2\zeta_{6}q^{7}+\cdots\)
975.2.b.e 975.b 13.b $2$ $7.785$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+2q^{4}-iq^{7}+q^{9}-iq^{11}+\cdots\)
975.2.b.f 975.b 13.b $4$ $7.785$ \(\Q(i, \sqrt{17})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{3}+(-3+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots\)
975.2.b.g 975.b 13.b $4$ $7.785$ 4.0.27648.1 None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
975.2.b.h 975.b 13.b $4$ $7.785$ 4.0.27648.1 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
975.2.b.i 975.b 13.b $6$ $7.785$ 6.0.559227904.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
975.2.b.j 975.b 13.b $6$ $7.785$ 6.0.50922496.1 None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{3}+(-1-\beta _{5})q^{4}-\beta _{2}q^{6}+\cdots\)
975.2.b.k 975.b 13.b $6$ $7.785$ 6.0.559227904.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
975.2.b.l 975.b 13.b $6$ $7.785$ 6.0.50922496.1 None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+q^{3}+(-1-\beta _{5})q^{4}+\beta _{2}q^{6}+\cdots\)

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

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