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Properties

Label 2415.2.bi
Level $2415$
Weight $2$
Character orbit 2415.bi
Rep. character $\chi_{2415}(1241,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $512$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2415.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 483 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2415, [\chi])\).

Total New Old
Modular forms 784 512 272
Cusp forms 752 512 240
Eisenstein series 32 0 32

Trace form

\( 512 q + 256 q^{4} + 8 q^{6} - 4 q^{9} + O(q^{10}) \) \( 512 q + 256 q^{4} + 8 q^{6} - 4 q^{9} - 224 q^{16} - 16 q^{18} + 12 q^{24} - 256 q^{25} + 24 q^{27} - 104 q^{36} + 24 q^{39} + 36 q^{46} - 160 q^{48} + 8 q^{49} + 16 q^{54} + 16 q^{55} + 32 q^{58} - 384 q^{64} + 28 q^{69} + 24 q^{70} + 104 q^{72} + 192 q^{78} + 28 q^{81} - 80 q^{82} - 116 q^{87} + 76 q^{93} - 112 q^{94} - 96 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2415, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2415, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2415, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)