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Properties

Label 3850.2.cw
Level $3850$
Weight $2$
Character orbit 3850.cw
Rep. character $\chi_{3850}(641,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1920$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3850.cw (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1925 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3850, [\chi])\).

Total New Old
Modular forms 5824 1920 3904
Cusp forms 5696 1920 3776
Eisenstein series 128 0 128

Trace form

\( 1920 q - 960 q^{4} - 4 q^{5} - 16 q^{6} - 4 q^{7} + 240 q^{9} + O(q^{10}) \) \( 1920 q - 960 q^{4} - 4 q^{5} - 16 q^{6} - 4 q^{7} + 240 q^{9} + 6 q^{10} - 4 q^{11} + 8 q^{15} - 960 q^{16} - 4 q^{17} - 32 q^{19} + 8 q^{20} - 28 q^{22} - 8 q^{23} + 8 q^{24} + 10 q^{25} + 2 q^{28} + 8 q^{30} + 2 q^{31} + 26 q^{33} + 52 q^{35} - 480 q^{36} + 2 q^{37} - 40 q^{39} + 6 q^{40} - 16 q^{41} - 10 q^{42} + 80 q^{43} - 4 q^{44} - 46 q^{45} - 4 q^{46} - 12 q^{49} - 48 q^{50} - 40 q^{53} + 32 q^{54} - 36 q^{55} - 88 q^{57} - 32 q^{58} - 4 q^{60} + 26 q^{61} - 12 q^{62} - 54 q^{63} + 1920 q^{64} - 8 q^{65} - 16 q^{66} - 64 q^{67} - 4 q^{68} - 54 q^{70} + 16 q^{71} - 24 q^{73} + 110 q^{75} + 64 q^{76} - 2 q^{77} + 8 q^{79} - 4 q^{80} + 256 q^{81} - 16 q^{82} - 4 q^{83} - 56 q^{85} - 24 q^{86} + 120 q^{87} + 14 q^{88} - 40 q^{89} - 32 q^{90} + 28 q^{91} + 16 q^{92} - 40 q^{93} + 32 q^{94} + 36 q^{95} + 8 q^{96} - 76 q^{97} - 8 q^{98} + 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3850, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1925, [\chi])\)\(^{\oplus 2}\)