↑

Properties

Label 1815.2.w
Level $1815$
Weight $2$
Character orbit 1815.w
Rep. character $\chi_{1815}(323,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1600$
Sturm bound $528$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.w (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 2304 1856 448
Cusp forms 1920 1600 320
Eisenstein series 384 256 128

Trace form

\( 1600 q + 10 q^{3} + 12 q^{6} + 20 q^{7} + O(q^{10}) \) \( 1600 q + 10 q^{3} + 12 q^{6} + 20 q^{7} + 40 q^{10} + 20 q^{12} + 4 q^{13} + 22 q^{15} + 328 q^{16} - 2 q^{18} + 24 q^{21} + 60 q^{25} + 22 q^{27} - 8 q^{28} + 26 q^{30} + 8 q^{31} + 124 q^{36} - 28 q^{37} - 52 q^{40} - 14 q^{42} - 52 q^{45} - 14 q^{48} + 116 q^{51} - 12 q^{52} - 30 q^{57} - 136 q^{58} - 98 q^{60} + 14 q^{63} - 400 q^{67} - 56 q^{70} - 92 q^{72} + 80 q^{73} + 38 q^{75} + 176 q^{76} - 100 q^{78} - 72 q^{81} - 28 q^{82} + 12 q^{85} + 36 q^{87} - 16 q^{90} - 128 q^{91} + 26 q^{93} - 152 q^{96} + 108 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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