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Properties

Label 1815.4.bu
Level $1815$
Weight $4$
Character orbit 1815.bu
Rep. character $\chi_{1815}(38,\cdot)$
Character field $\Q(\zeta_{220})$
Dimension $63040$
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.bu (of order \(220\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1815 \)
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 63680 0
Cusp forms 63040 63040 0
Eisenstein series 640 640 0

Trace form

\( 63040 q - 60 q^{3} - 164 q^{6} - 188 q^{7} + O(q^{10}) \) \( 63040 q - 60 q^{3} - 164 q^{6} - 188 q^{7} - 72 q^{10} - 526 q^{12} - 596 q^{13} - 82 q^{15} - 25160 q^{16} + 62 q^{18} - 368 q^{21} + 928 q^{22} - 380 q^{25} - 60 q^{27} + 716 q^{28} + 418 q^{30} + 104 q^{31} + 864 q^{33} - 2868 q^{36} - 596 q^{37} - 2184 q^{40} + 708 q^{42} - 2160 q^{43} + 1250 q^{45} - 760 q^{46} + 852 q^{48} + 13844 q^{51} - 92 q^{52} - 3608 q^{55} - 904 q^{57} + 3300 q^{58} + 5010 q^{60} - 40 q^{61} - 1036 q^{63} + 1884 q^{66} + 240 q^{67} - 12468 q^{70} + 11492 q^{72} + 5800 q^{73} - 3634 q^{75} - 560 q^{76} + 3858 q^{78} - 2072 q^{81} - 5068 q^{82} + 1996 q^{85} - 802 q^{87} - 22848 q^{88} - 6782 q^{90} + 18104 q^{91} - 8408 q^{93} + 7496 q^{96} - 4220 q^{97} + O(q^{100}) \)

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.