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Properties

Label 3850.2.q
Level $3850$
Weight $2$
Character orbit 3850.q
Rep. character $\chi_{3850}(71,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $720$
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.q (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 2912 720 2192
Cusp forms 2848 720 2128
Eisenstein series 64 0 64

Trace form

\( 720 q - 12 q^{3} + 720 q^{4} + 4 q^{5} - 192 q^{9} + O(q^{10}) \) \( 720 q - 12 q^{3} + 720 q^{4} + 4 q^{5} - 192 q^{9} - 12 q^{12} - 48 q^{13} + 24 q^{15} + 720 q^{16} + 32 q^{19} + 4 q^{20} + 8 q^{21} + 8 q^{22} + 8 q^{23} - 4 q^{25} + 12 q^{27} - 96 q^{29} + 32 q^{30} + 24 q^{31} + 40 q^{33} - 192 q^{36} + 20 q^{37} + 48 q^{38} + 32 q^{43} + 44 q^{45} + 12 q^{46} - 12 q^{48} - 180 q^{49} + 16 q^{50} + 16 q^{51} - 48 q^{52} + 36 q^{53} - 12 q^{54} + 52 q^{55} + 60 q^{57} + 56 q^{59} + 24 q^{60} - 16 q^{61} + 32 q^{62} + 720 q^{64} - 56 q^{65} - 108 q^{67} + 80 q^{69} - 12 q^{70} + 64 q^{71} - 12 q^{73} + 40 q^{74} - 20 q^{75} + 32 q^{76} + 16 q^{77} + 28 q^{78} + 4 q^{80} - 216 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} + 40 q^{85} + 32 q^{87} + 8 q^{88} + 40 q^{89} + 40 q^{90} + 8 q^{92} + 24 q^{93} + 88 q^{95} + 28 q^{97} - 8 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1925, [\chi])\)\(^{\oplus 2}\)