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Properties

Label 912.4.cs
Level $912$
Weight $4$
Character orbit 912.cs
Rep. character $\chi_{912}(29,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $5712$
Sturm bound $640$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 912.cs (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 912 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(912, [\chi])\).

Total New Old
Modular forms 5808 5808 0
Cusp forms 5712 5712 0
Eisenstein series 96 96 0

Trace form

\( 5712 q - 12 q^{3} - 24 q^{4} - 12 q^{6} + O(q^{10}) \) \( 5712 q - 12 q^{3} - 24 q^{4} - 12 q^{6} + 156 q^{10} - 18 q^{12} - 24 q^{13} - 24 q^{15} - 420 q^{16} - 24 q^{19} - 174 q^{21} - 24 q^{22} - 12 q^{24} - 18 q^{27} - 792 q^{28} - 804 q^{30} - 72 q^{31} - 24 q^{33} - 24 q^{34} - 12 q^{36} - 24 q^{40} - 3348 q^{42} - 24 q^{43} - 6 q^{45} - 36 q^{46} - 12 q^{48} + 132864 q^{49} - 12 q^{51} + 1272 q^{52} + 318 q^{54} - 48 q^{58} + 4566 q^{60} - 24 q^{61} - 4140 q^{63} - 12 q^{64} + 3288 q^{66} - 24 q^{67} - 18 q^{69} - 2628 q^{70} + 2880 q^{72} - 2184 q^{76} - 108 q^{78} - 48 q^{79} - 24 q^{81} - 24 q^{82} - 18 q^{84} - 1464 q^{85} - 36 q^{88} - 7032 q^{90} - 4140 q^{91} - 174 q^{93} + 828 q^{96} - 48 q^{97} + 4362 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.