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Properties

Label 3850.2.ch
Level $3850$
Weight $2$
Character orbit 3850.ch
Rep. character $\chi_{3850}(309,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $592$
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.ch (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
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 592 2320
Cusp forms 2848 592 2256
Eisenstein series 64 0 64

Trace form

\( 592 q + 148 q^{4} - 16 q^{5} + 132 q^{9} + O(q^{10}) \) \( 592 q + 148 q^{4} - 16 q^{5} + 132 q^{9} + 8 q^{10} + 4 q^{11} - 20 q^{12} - 8 q^{14} - 32 q^{15} - 148 q^{16} - 4 q^{20} + 40 q^{23} + 64 q^{25} - 16 q^{26} + 60 q^{27} + 40 q^{29} + 8 q^{30} + 24 q^{31} + 8 q^{35} - 132 q^{36} - 40 q^{37} + 24 q^{39} - 8 q^{40} - 16 q^{41} - 4 q^{44} - 44 q^{45} - 200 q^{47} - 20 q^{48} - 592 q^{49} + 8 q^{50} + 80 q^{51} - 40 q^{53} - 12 q^{55} + 8 q^{56} + 12 q^{59} + 12 q^{60} + 40 q^{63} + 148 q^{64} + 160 q^{65} - 60 q^{67} - 68 q^{69} - 40 q^{71} + 160 q^{73} + 16 q^{74} - 8 q^{75} + 80 q^{79} + 4 q^{80} - 216 q^{81} - 120 q^{83} + 56 q^{85} + 40 q^{86} - 32 q^{89} - 64 q^{90} + 8 q^{91} - 20 q^{92} - 32 q^{95} - 120 q^{97} + 88 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1925, [\chi])\)\(^{\oplus 2}\)