Properties

Label 1476.2.bp
Level $1476$
Weight $2$
Character orbit 1476.bp
Rep. character $\chi_{1476}(79,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $1984$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1476 = 2^{2} \cdot 3^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1476.bp (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1476 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1476, [\chi])\).

Total New Old
Modular forms 2048 2048 0
Cusp forms 1984 1984 0
Eisenstein series 64 64 0

Trace form

\( 1984 q - 4 q^{2} - 8 q^{5} - 20 q^{6} - 16 q^{8} - 24 q^{9} + O(q^{10}) \) \( 1984 q - 4 q^{2} - 8 q^{5} - 20 q^{6} - 16 q^{8} - 24 q^{9} - 32 q^{10} - 20 q^{12} - 8 q^{13} - 4 q^{14} - 8 q^{16} - 16 q^{17} - 16 q^{18} - 36 q^{20} - 16 q^{21} - 4 q^{22} - 8 q^{24} - 16 q^{26} + 16 q^{28} - 8 q^{29} + 16 q^{30} - 44 q^{32} + 64 q^{33} - 4 q^{34} - 12 q^{36} - 64 q^{37} - 44 q^{38} - 8 q^{41} + 144 q^{42} + 16 q^{44} - 60 q^{48} - 8 q^{49} - 40 q^{50} - 36 q^{52} - 32 q^{53} - 120 q^{54} - 84 q^{56} - 32 q^{57} - 4 q^{58} - 72 q^{60} - 8 q^{61} - 24 q^{62} - 8 q^{65} + 12 q^{68} + 8 q^{69} + 24 q^{70} - 32 q^{73} - 12 q^{74} - 20 q^{76} - 8 q^{77} + 40 q^{78} + 24 q^{80} - 16 q^{82} - 80 q^{84} - 8 q^{85} + 44 q^{88} - 68 q^{90} - 56 q^{92} + 8 q^{93} - 16 q^{94} - 16 q^{96} - 8 q^{97} - 32 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1476, [\chi])\) into newform subspaces

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