↑

Properties

Label 1815.2.bu
Level $1815$
Weight $2$
Character orbit 1815.bu
Rep. character $\chi_{1815}(38,\cdot)$
Character field $\Q(\zeta_{220})$
Dimension $20800$
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.bu (of order \(220\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1815 \)
Character field: \(\Q(\zeta_{220})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 21440 21440 0
Cusp forms 20800 20800 0
Eisenstein series 640 640 0

Trace form

\( 20800 q - 60 q^{3} - 164 q^{6} - 156 q^{7} + O(q^{10}) \) \( 20800 q - 60 q^{3} - 164 q^{6} - 156 q^{7} - 92 q^{10} - 118 q^{12} - 128 q^{13} - 82 q^{15} - 824 q^{16} - 46 q^{18} - 152 q^{21} - 244 q^{22} - 140 q^{25} - 60 q^{27} - 184 q^{28} - 62 q^{30} - 344 q^{31} - 192 q^{33} - 228 q^{36} - 180 q^{37} - 184 q^{40} - 96 q^{42} - 176 q^{43} + 50 q^{45} - 352 q^{46} - 36 q^{48} - 148 q^{51} - 188 q^{52} - 8 q^{55} - 184 q^{57} - 264 q^{58} - 90 q^{60} - 352 q^{61} - 118 q^{63} - 156 q^{66} - 192 q^{67} - 288 q^{70} - 4 q^{72} - 96 q^{73} - 34 q^{75} - 176 q^{76} - 174 q^{78} - 164 q^{81} - 172 q^{82} - 164 q^{85} + 14 q^{87} + 100 q^{88} - 302 q^{90} - 744 q^{91} - 32 q^{93} - 328 q^{96} - 92 q^{97} + O(q^{100}) \)

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.