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Properties

Label 975.2.cs
Level $975$
Weight $2$
Character orbit 975.cs
Rep. character $\chi_{975}(113,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $2176$
Newform subspaces $1$
Sturm bound $280$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 975.cs (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 975 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 1 \)
Sturm bound: \(280\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 2304 2304 0
Cusp forms 2176 2176 0
Eisenstein series 128 128 0

Trace form

\( 2176 q - 8 q^{3} - 20 q^{4} - 6 q^{6} - 16 q^{7} - 10 q^{9} + O(q^{10}) \) \( 2176 q - 8 q^{3} - 20 q^{4} - 6 q^{6} - 16 q^{7} - 10 q^{9} - 8 q^{10} - 12 q^{12} - 16 q^{13} - 8 q^{15} - 260 q^{16} - 56 q^{18} - 60 q^{19} - 24 q^{21} - 8 q^{22} - 64 q^{25} - 8 q^{27} + 24 q^{28} - 6 q^{30} - 48 q^{31} + 36 q^{33} - 160 q^{34} + 26 q^{36} - 40 q^{37} - 60 q^{39} - 24 q^{40} - 18 q^{42} - 4 q^{43} + 12 q^{45} - 12 q^{46} + 96 q^{48} - 64 q^{51} - 4 q^{52} + 120 q^{54} - 20 q^{55} - 108 q^{57} - 136 q^{60} - 12 q^{61} - 2 q^{63} - 240 q^{64} + 24 q^{66} + 32 q^{67} - 80 q^{69} + 104 q^{70} - 16 q^{72} - 144 q^{73} + 34 q^{75} + 32 q^{76} - 94 q^{78} - 80 q^{79} - 6 q^{81} - 88 q^{82} - 10 q^{84} - 152 q^{85} + 76 q^{87} + 96 q^{88} - 92 q^{90} - 24 q^{91} - 42 q^{93} - 300 q^{94} - 120 q^{96} - 68 q^{97} + O(q^{100}) \)

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.cs.a 975.cs 975.bs $2176$ $7.785$ None \(0\) \(-8\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{60}]$