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Properties

Label 3850.2.ba
Level $3850$
Weight $2$
Character orbit 3850.ba
Rep. character $\chi_{3850}(1709,\cdot)$
Character field $\Q(\zeta_{10})$
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.ba (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 275 \)
Character field: \(\Q(\zeta_{10})\)
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

\( 720 q + 180 q^{4} - 4 q^{5} - 712 q^{9} + O(q^{10}) \) \( 720 q + 180 q^{4} - 4 q^{5} - 712 q^{9} + 20 q^{12} + 44 q^{15} - 180 q^{16} - 8 q^{19} + 4 q^{20} - 8 q^{21} + 24 q^{25} + 24 q^{29} - 16 q^{30} + 36 q^{31} - 188 q^{36} + 20 q^{37} - 60 q^{38} - 20 q^{45} - 32 q^{46} + 180 q^{49} + 16 q^{50} - 16 q^{51} - 60 q^{53} - 12 q^{54} + 12 q^{55} + 20 q^{57} - 24 q^{59} + 16 q^{60} - 64 q^{61} - 40 q^{62} + 180 q^{64} + 88 q^{65} + 100 q^{67} - 60 q^{69} + 8 q^{70} - 84 q^{71} - 60 q^{73} + 40 q^{74} + 92 q^{75} - 32 q^{76} + 100 q^{78} - 4 q^{80} + 736 q^{81} - 40 q^{82} - 100 q^{83} + 8 q^{84} + 72 q^{85} - 20 q^{88} - 40 q^{89} - 40 q^{90} + 80 q^{93} - 44 q^{95} - 8 q^{99} + O(q^{100}) \)

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

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