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Properties

Label 3332.2.bl
Level $3332$
Weight $2$
Character orbit 3332.bl
Rep. character $\chi_{3332}(99,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $2872$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3332.bl (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 68 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3332, [\chi])\).

Total New Old
Modular forms 4160 3032 1128
Cusp forms 3904 2872 1032
Eisenstein series 256 160 96

Trace form

\( 2872 q + 8 q^{2} + 8 q^{4} + 16 q^{5} + 8 q^{6} - 40 q^{8} + 16 q^{9} + O(q^{10}) \) \( 2872 q + 8 q^{2} + 8 q^{4} + 16 q^{5} + 8 q^{6} - 40 q^{8} + 16 q^{9} + 8 q^{10} + 8 q^{12} + 16 q^{13} + 16 q^{17} + 16 q^{18} + 8 q^{20} - 40 q^{22} + 24 q^{24} + 16 q^{25} - 24 q^{26} - 80 q^{29} - 56 q^{30} + 48 q^{32} + 72 q^{34} + 24 q^{36} + 16 q^{37} + 48 q^{38} - 56 q^{40} + 16 q^{41} - 24 q^{44} + 16 q^{45} + 24 q^{46} + 32 q^{48} + 16 q^{52} + 24 q^{53} + 24 q^{54} - 48 q^{58} - 96 q^{60} - 16 q^{61} + 64 q^{62} - 88 q^{64} + 120 q^{65} - 112 q^{66} + 96 q^{68} - 32 q^{69} - 96 q^{72} + 120 q^{73} - 40 q^{74} + 64 q^{76} - 144 q^{78} - 88 q^{80} + 96 q^{81} + 48 q^{82} - 72 q^{85} - 64 q^{86} + 72 q^{88} + 16 q^{89} + 168 q^{90} - 152 q^{92} + 16 q^{93} - 88 q^{94} + 160 q^{96} + 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3332, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3332, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3332, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)