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Properties

Label 3380.2.bc
Level $3380$
Weight $2$
Character orbit 3380.bc
Rep. character $\chi_{3380}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1768$
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.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1092\)

Dimensions

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

Total New Old
Modular forms 2296 1928 368
Cusp forms 2072 1768 304
Eisenstein series 224 160 64

Trace form

\( 1768 q + 12 q^{4} + 10 q^{5} - 796 q^{9} + O(q^{10}) \) \( 1768 q + 12 q^{4} + 10 q^{5} - 796 q^{9} + 6 q^{10} - 64 q^{14} + 36 q^{16} + 2 q^{20} - 8 q^{21} + 28 q^{24} + 8 q^{29} + 6 q^{30} + 16 q^{34} - 24 q^{36} + 32 q^{40} + 48 q^{41} - 44 q^{45} - 64 q^{46} + 24 q^{49} + 64 q^{50} - 80 q^{54} - 96 q^{56} + 48 q^{60} + 28 q^{61} - 168 q^{66} + 24 q^{69} + 80 q^{70} + 4 q^{74} + 28 q^{76} + 52 q^{80} - 532 q^{81} - 84 q^{84} - 26 q^{85} + 52 q^{86} + 52 q^{89} + 116 q^{94} + 124 q^{96} + O(q^{100}) \)

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

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