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Properties

Label 3380.2.bx
Level $3380$
Weight $2$
Character orbit 3380.bx
Rep. character $\chi_{3380}(359,\cdot)$
Character field $\Q(\zeta_{52})$
Dimension $13008$
Sturm bound $1092$

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Defining parameters

Level: \( N \) \(=\) \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3380.bx (of order \(52\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3380 \)
Character field: \(\Q(\zeta_{52})\)
Sturm bound: \(1092\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3380, [\chi])\).

Total New Old
Modular forms 13200 13200 0
Cusp forms 13008 13008 0
Eisenstein series 192 192 0

Trace form

\( 13008 q - 52 q^{4} - 50 q^{5} - 40 q^{6} - 1156 q^{9} + O(q^{10}) \) \( 13008 q - 52 q^{4} - 50 q^{5} - 40 q^{6} - 1156 q^{9} - 26 q^{10} - 60 q^{14} - 44 q^{16} - 22 q^{20} - 72 q^{21} - 20 q^{24} - 52 q^{25} - 32 q^{26} - 88 q^{29} - 26 q^{30} - 32 q^{34} - 52 q^{36} - 62 q^{40} - 68 q^{41} - 40 q^{44} - 26 q^{45} + 8 q^{46} - 104 q^{49} - 18 q^{50} + 64 q^{54} - 52 q^{56} + 22 q^{60} - 48 q^{61} - 52 q^{64} - 58 q^{65} - 176 q^{66} + 208 q^{69} + 2 q^{70} - 44 q^{74} - 68 q^{76} + 42 q^{80} - 1060 q^{81} - 40 q^{84} - 20 q^{85} - 68 q^{86} - 156 q^{89} - 26 q^{90} - 76 q^{94} - 56 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3380, [\chi])\) into newform subspaces

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