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Properties

Label 3380.2.u
Level $3380$
Weight $2$
Character orbit 3380.u
Rep. character $\chi_{3380}(99,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $884$
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.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
Character field: \(\Q(i)\)
Sturm bound: \(1092\)

Dimensions

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

Total New Old
Modular forms 1148 964 184
Cusp forms 1036 884 152
Eisenstein series 112 80 32

Trace form

\( 884 q + 2 q^{5} + 12 q^{6} + 820 q^{9} + O(q^{10}) \) \( 884 q + 2 q^{5} + 12 q^{6} + 820 q^{9} - 56 q^{14} - 24 q^{16} + 4 q^{20} + 32 q^{21} + 32 q^{24} + 16 q^{29} + 20 q^{34} - 44 q^{40} + 36 q^{41} + 12 q^{44} + 26 q^{45} - 44 q^{46} + 8 q^{50} + 116 q^{54} + 48 q^{60} + 56 q^{61} - 48 q^{66} + 28 q^{70} + 8 q^{74} - 16 q^{76} + 68 q^{80} + 628 q^{81} + 12 q^{84} + 32 q^{85} - 16 q^{86} - 52 q^{89} - 152 q^{94} - 4 q^{96} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(3380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 2}\)