Properties

Label 1815.2.bm
Level $1815$
Weight $2$
Character orbit 1815.bm
Rep. character $\chi_{1815}(4,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $5280$
Sturm bound $528$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.bm (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{110})\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1815, [\chi])\).

Total New Old
Modular forms 10720 5280 5440
Cusp forms 10400 5280 5120
Eisenstein series 320 0 320

Trace form

\( 5280q - 132q^{4} + 4q^{5} - 4q^{6} + 1320q^{9} + O(q^{10}) \) \( 5280q - 132q^{4} + 4q^{5} - 4q^{6} + 1320q^{9} - 10q^{10} + 44q^{11} + 12q^{14} - 10q^{15} + 156q^{16} + 16q^{19} - 46q^{20} + 32q^{21} + 12q^{24} - 14q^{25} + 68q^{26} - 4q^{30} + 20q^{31} - 8q^{34} + 40q^{35} + 132q^{36} + 8q^{39} + 72q^{40} - 60q^{41} + 48q^{44} - 4q^{45} - 108q^{46} - 48q^{49} + 82q^{50} - 28q^{51} - 16q^{54} - 68q^{55} - 192q^{56} - 44q^{59} - 36q^{60} - 40q^{61} - 192q^{64} + 46q^{65} - 12q^{66} - 20q^{69} - 126q^{70} + 192q^{71} + 32q^{74} + 32q^{75} + 224q^{76} + 96q^{79} - 62q^{80} - 1320q^{81} - 18q^{85} + 136q^{86} - 40q^{89} + 30q^{90} + 40q^{91} - 248q^{94} + 2q^{95} - 28q^{96} - 44q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1815, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1815, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)