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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

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

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

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