Properties

Label 1815.2.p
Level $1815$
Weight $2$
Character orbit 1815.p
Rep. character $\chi_{1815}(161,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $576$
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.p (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 1152 576 576
Cusp forms 960 576 384
Eisenstein series 192 0 192

Trace form

\( 576q - 4q^{3} - 144q^{4} + 10q^{6} + 18q^{9} + O(q^{10}) \) \( 576q - 4q^{3} - 144q^{4} + 10q^{6} + 18q^{9} - 12q^{12} + 6q^{15} - 176q^{16} + 10q^{18} + 60q^{19} - 30q^{24} + 144q^{25} - 10q^{27} + 80q^{28} - 20q^{31} - 104q^{34} - 74q^{36} + 4q^{37} + 10q^{39} + 82q^{42} + 20q^{46} + 78q^{48} + 152q^{49} + 30q^{51} + 30q^{57} - 80q^{58} - 58q^{60} - 20q^{61} - 50q^{63} - 220q^{64} + 88q^{67} - 30q^{69} - 36q^{70} + 120q^{72} - 40q^{73} - 6q^{75} + 52q^{78} + 140q^{79} - 50q^{81} - 24q^{82} + 80q^{84} + 4q^{91} - 92q^{93} + 40q^{94} - 10q^{96} + 132q^{97} + O(q^{100}) \)

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

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