↑

Properties

Label 2415.2.bt
Level $2415$
Weight $2$
Character orbit 2415.bt
Rep. character $\chi_{2415}(298,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $768$
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.bt (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 805 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 1568 768 800
Cusp forms 1504 768 736
Eisenstein series 64 0 64

Trace form

\( 768 q + O(q^{10}) \) \( 768 q + 384 q^{16} + 24 q^{23} - 8 q^{25} + 16 q^{26} - 8 q^{31} - 8 q^{35} + 768 q^{36} - 128 q^{41} + 56 q^{46} - 8 q^{47} + 64 q^{48} + 144 q^{50} + 152 q^{52} - 32 q^{58} + 192 q^{62} + 16 q^{70} + 16 q^{71} + 24 q^{73} - 32 q^{75} - 184 q^{77} + 32 q^{78} + 384 q^{81} + 8 q^{82} + 144 q^{85} - 24 q^{87} - 216 q^{92} + 48 q^{93} + 72 q^{95} - 144 q^{98} + O(q^{100}) \)

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

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