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Properties

Label 1815.4.bt
Level $1815$
Weight $4$
Character orbit 1815.bt
Rep. character $\chi_{1815}(7,\cdot)$
Character field $\Q(\zeta_{220})$
Dimension $31680$
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.bt (of order \(220\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{220})\)
Sturm bound: \(1056\)

Dimensions

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

Total New Old
Modular forms 63680 31680 32000
Cusp forms 63040 31680 31360
Eisenstein series 640 0 640

Trace form

\( 31680 q - 32 q^{5} + 40 q^{7} + O(q^{10}) \) \( 31680 q - 32 q^{5} + 40 q^{7} - 264 q^{10} + 56 q^{11} - 48 q^{12} + 528 q^{13} + 252 q^{15} - 12672 q^{16} + 640 q^{17} - 1140 q^{20} + 1228 q^{22} + 224 q^{23} + 232 q^{25} - 608 q^{26} - 720 q^{28} + 2040 q^{30} + 432 q^{31} + 228 q^{33} - 28512 q^{36} - 2592 q^{37} + 2072 q^{38} - 4440 q^{41} - 1224 q^{42} - 9600 q^{46} + 2280 q^{47} + 576 q^{48} + 18340 q^{50} + 1680 q^{51} + 8520 q^{52} + 1872 q^{53} - 5084 q^{55} + 3408 q^{56} + 1920 q^{57} - 784 q^{58} + 1152 q^{60} + 480 q^{61} - 160 q^{62} - 360 q^{63} - 1128 q^{66} + 8736 q^{67} - 10240 q^{68} - 13752 q^{70} + 7380 q^{73} - 96 q^{75} + 17952 q^{76} - 3312 q^{77} - 7680 q^{80} + 641520 q^{81} + 2984 q^{82} - 13400 q^{83} + 384 q^{85} + 10592 q^{86} - 7188 q^{88} - 8232 q^{91} - 1740 q^{92} - 4104 q^{93} - 2760 q^{95} - 9744 q^{97} + O(q^{100}) \)

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

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