Properties

Label 1815.2.s
Level $1815$
Weight $2$
Character orbit 1815.s
Rep. character $\chi_{1815}(124,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $432$
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.s (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 1152 432 720
Cusp forms 960 432 528
Eisenstein series 192 0 192

Trace form

\( 432q + 108q^{4} + 4q^{5} - 4q^{6} + 108q^{9} + O(q^{10}) \) \( 432q + 108q^{4} + 4q^{5} - 4q^{6} + 108q^{9} + 12q^{10} - 4q^{14} - 10q^{15} - 68q^{16} + 16q^{19} - 46q^{20} + 32q^{21} + 12q^{24} - 14q^{25} + 84q^{26} - 4q^{30} + 20q^{31} + 56q^{34} + 40q^{35} - 108q^{36} + 8q^{39} + 72q^{40} - 60q^{41} - 4q^{45} - 108q^{46} + 148q^{49} + 38q^{50} - 28q^{51} - 16q^{54} - 120q^{56} - 76q^{59} - 60q^{60} - 40q^{61} + 64q^{64} - 20q^{65} - 20q^{69} - 90q^{70} + 48q^{71} + 32q^{74} + 48q^{75} + 136q^{76} + 52q^{79} - 22q^{80} - 108q^{81} + 70q^{85} + 72q^{86} - 40q^{89} + 8q^{90} + 40q^{91} - 72q^{94} + 2q^{95} - 28q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)