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Properties

Label 1815.4.bi
Level $1815$
Weight $4$
Character orbit 1815.bi
Rep. character $\chi_{1815}(43,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $7920$
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.bi (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(1056\)

Dimensions

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

Total New Old
Modular forms 15920 7920 8000
Cusp forms 15760 7920 7840
Eisenstein series 160 0 160

Trace form

\( 7920 q + 32 q^{5} + O(q^{10}) \) \( 7920 q + 32 q^{5} + 264 q^{10} - 56 q^{11} + 48 q^{12} - 528 q^{13} + 168 q^{15} + 12672 q^{16} - 760 q^{20} - 1228 q^{22} - 224 q^{23} - 592 q^{25} + 608 q^{26} - 432 q^{31} - 228 q^{33} + 28512 q^{36} + 2592 q^{37} - 2072 q^{38} - 816 q^{42} - 2400 q^{47} + 384 q^{48} - 15620 q^{50} + 1248 q^{53} + 7244 q^{55} - 3408 q^{56} + 1624 q^{58} + 768 q^{60} - 1992 q^{66} - 8736 q^{67} + 5952 q^{70} + 96 q^{75} - 17952 q^{76} + 3312 q^{77} - 5120 q^{80} - 641520 q^{81} + 5296 q^{82} - 704 q^{85} - 10592 q^{86} + 3708 q^{88} - 1088 q^{91} - 17960 q^{92} - 2736 q^{93} + 4104 q^{97} + O(q^{100}) \)

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

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