Properties

Label 1815.2.u
Level $1815$
Weight $2$
Character orbit 1815.u
Rep. character $\chi_{1815}(166,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $880$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.u (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 2680 880 1800
Cusp forms 2600 880 1720
Eisenstein series 80 0 80

Trace form

\( 880q + 8q^{2} - 80q^{4} + 8q^{7} + 24q^{8} + 880q^{9} + O(q^{10}) \) \( 880q + 8q^{2} - 80q^{4} + 8q^{7} + 24q^{8} + 880q^{9} + 4q^{10} + 16q^{11} - 28q^{13} - 56q^{14} - 64q^{16} + 24q^{17} + 8q^{18} + 8q^{19} + 28q^{22} - 64q^{23} + 24q^{24} - 88q^{25} + 8q^{26} + 48q^{28} + 48q^{29} + 4q^{30} - 20q^{31} + 96q^{32} + 4q^{33} + 72q^{34} + 8q^{35} - 80q^{36} + 40q^{37} + 56q^{38} + 8q^{39} - 120q^{40} + 32q^{41} + 24q^{42} + 40q^{43} + 28q^{44} + 64q^{46} + 32q^{47} + 32q^{48} - 84q^{49} + 8q^{50} + 16q^{51} - 156q^{52} - 176q^{53} + 8q^{55} + 52q^{56} + 8q^{57} - 68q^{58} + 40q^{59} + 80q^{61} - 164q^{62} + 8q^{63} - 72q^{64} + 24q^{65} + 40q^{66} - 20q^{67} + 80q^{68} + 8q^{69} + 24q^{70} + 40q^{71} + 24q^{72} + 20q^{73} + 96q^{74} - 12q^{76} + 88q^{77} - 156q^{78} - 132q^{79} + 880q^{81} + 48q^{82} + 56q^{83} + 72q^{84} + 8q^{85} + 88q^{86} + 32q^{87} + 92q^{88} - 80q^{89} + 4q^{90} - 36q^{91} + 136q^{92} + 16q^{93} - 32q^{94} - 176q^{96} - 100q^{97} - 256q^{98} + 16q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)