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Properties

Label 1815.2.m
Level $1815$
Weight $2$
Character orbit 1815.m
Rep. character $\chi_{1815}(511,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $288$
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.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 1152 288 864
Cusp forms 960 288 672
Eisenstein series 192 0 192

Trace form

\( 288 q - 8 q^{2} - 80 q^{4} - 8 q^{7} + 16 q^{8} - 72 q^{9} + O(q^{10}) \) \( 288 q - 8 q^{2} - 80 q^{4} - 8 q^{7} + 16 q^{8} - 72 q^{9} + 16 q^{10} + 4 q^{13} - 8 q^{14} - 72 q^{16} + 16 q^{17} + 12 q^{18} - 8 q^{19} - 16 q^{20} + 40 q^{23} + 36 q^{24} - 72 q^{25} - 40 q^{26} - 28 q^{28} - 8 q^{29} - 4 q^{30} - 20 q^{31} - 56 q^{32} + 56 q^{34} - 8 q^{35} - 80 q^{36} + 44 q^{37} + 28 q^{38} - 8 q^{39} - 12 q^{40} + 28 q^{41} - 40 q^{42} + 40 q^{43} - 24 q^{46} + 16 q^{47} - 32 q^{48} - 92 q^{49} - 8 q^{50} + 4 q^{51} - 52 q^{52} - 24 q^{53} + 96 q^{56} - 8 q^{57} + 4 q^{58} - 88 q^{59} - 20 q^{61} - 16 q^{62} - 8 q^{63} - 68 q^{64} - 24 q^{65} + 40 q^{67} + 40 q^{68} - 24 q^{69} + 20 q^{70} - 48 q^{71} - 4 q^{72} + 36 q^{73} + 84 q^{74} + 40 q^{76} - 64 q^{78} + 32 q^{79} - 32 q^{80} - 72 q^{81} + 28 q^{82} + 4 q^{83} + 48 q^{84} - 8 q^{85} + 40 q^{86} + 88 q^{87} + 160 q^{89} - 4 q^{90} + 68 q^{91} + 56 q^{92} + 40 q^{93} + 36 q^{94} + 12 q^{96} - 20 q^{97} - 96 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)