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Properties

Label 2415.2.bh
Level $2415$
Weight $2$
Character orbit 2415.bh
Rep. character $\chi_{2415}(1864,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $352$
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.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 784 352 432
Cusp forms 752 352 400
Eisenstein series 32 0 32

Trace form

\( 352 q + 176 q^{4} + 16 q^{6} + 176 q^{9} + O(q^{10}) \) \( 352 q + 176 q^{4} + 16 q^{6} + 176 q^{9} + 8 q^{10} + 56 q^{14} + 8 q^{15} - 192 q^{16} + 8 q^{19} + 48 q^{20} + 8 q^{21} + 24 q^{24} + 12 q^{25} + 32 q^{26} - 8 q^{29} - 28 q^{31} - 32 q^{34} + 352 q^{36} + 8 q^{39} - 12 q^{40} - 64 q^{41} + 16 q^{44} + 12 q^{49} + 40 q^{50} + 8 q^{54} - 48 q^{56} + 36 q^{59} - 12 q^{60} - 8 q^{61} - 512 q^{64} - 28 q^{65} - 24 q^{66} - 32 q^{69} - 64 q^{70} + 104 q^{71} - 40 q^{74} - 80 q^{76} + 8 q^{79} - 28 q^{80} - 176 q^{81} + 40 q^{84} + 16 q^{85} + 16 q^{90} + 24 q^{91} + 72 q^{94} + 24 q^{95} - 56 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2415, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(805, [\chi])\)\(^{\oplus 2}\)