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Properties

Label 1815.4.r
Level $1815$
Weight $4$
Character orbit 1815.r
Rep. character $\chi_{1815}(239,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $2528$
Sturm bound $1056$

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Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1815.r (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 165 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1056\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1815, [\chi])\).

Total New Old
Modular forms 3264 2656 608
Cusp forms 3072 2528 544
Eisenstein series 192 128 64

Trace form

\( 2528 q + 2476 q^{4} + 10 q^{6} - 106 q^{9} + O(q^{10}) \) \( 2528 q + 2476 q^{4} + 10 q^{6} - 106 q^{9} + 25 q^{15} - 9052 q^{16} + 20 q^{19} + 90 q^{24} + 6 q^{25} + 920 q^{30} + 768 q^{31} - 208 q^{34} - 18 q^{36} - 910 q^{39} - 1350 q^{40} - 4250 q^{45} - 180 q^{46} - 25940 q^{49} - 510 q^{51} + 806 q^{60} + 260 q^{61} + 31352 q^{64} + 1560 q^{69} + 3528 q^{70} + 223 q^{75} - 2320 q^{79} - 1066 q^{81} - 8540 q^{84} - 8210 q^{85} - 6540 q^{90} - 1124 q^{91} + 6260 q^{94} - 7610 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1815, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1815, [\chi])\) into lower level spaces

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