Properties

Label 1815.2.r
Level $1815$
Weight $2$
Character orbit 1815.r
Rep. character $\chi_{1815}(239,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $800$
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.r (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
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 928 224
Cusp forms 960 800 160
Eisenstein series 192 128 64

Trace form

\( 800q + 196q^{4} + 10q^{6} + 8q^{9} + O(q^{10}) \) \( 800q + 196q^{4} + 10q^{6} + 8q^{9} + 7q^{15} - 100q^{16} + 20q^{19} + 30q^{24} - 12q^{25} - 10q^{30} + 8q^{31} - 104q^{34} + 6q^{36} + 50q^{39} - 60q^{40} + 88q^{45} + 40q^{46} - 172q^{49} - 30q^{51} - 28q^{60} + 8q^{64} - 60q^{69} + 26q^{70} - 29q^{75} + 56q^{81} - 140q^{84} + 30q^{85} - 120q^{90} - 64q^{91} - 60q^{94} + 70q^{96} + O(q^{100}) \)

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

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