↑

Properties

Label 2415.2.be
Level $2415$
Weight $2$
Character orbit 2415.be
Rep. character $\chi_{2415}(1634,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $704$
Sturm bound $768$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2415.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
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 784 704 80
Cusp forms 752 704 48
Eisenstein series 32 0 32

Trace form

\( 704 q - 352 q^{4} + 4 q^{9} + O(q^{10}) \) \( 704 q - 352 q^{4} + 4 q^{9} - 12 q^{10} + 12 q^{15} - 352 q^{16} - 24 q^{19} + 12 q^{21} + 12 q^{25} - 32 q^{30} - 24 q^{31} - 112 q^{36} - 8 q^{39} + 36 q^{40} + 30 q^{45} - 16 q^{49} - 4 q^{51} + 84 q^{54} - 4 q^{60} - 24 q^{61} + 656 q^{64} + 96 q^{66} - 140 q^{70} - 126 q^{75} - 112 q^{79} + 12 q^{81} - 128 q^{84} - 16 q^{85} + 72 q^{91} - 24 q^{94} + 84 q^{96} + 8 q^{99} + O(q^{100}) \)

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

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