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Properties

Label 3850.2.i
Level $3850$
Weight $2$
Character orbit 3850.i
Rep. character $\chi_{3850}(1101,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $256$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1488 256 1232
Cusp forms 1392 256 1136
Eisenstein series 96 0 96

Trace form

\( 256 q - 128 q^{4} - 8 q^{6} - 8 q^{7} - 128 q^{9} + O(q^{10}) \) \( 256 q - 128 q^{4} - 8 q^{6} - 8 q^{7} - 128 q^{9} + 8 q^{13} + 8 q^{14} - 128 q^{16} + 12 q^{17} - 8 q^{18} - 8 q^{19} + 8 q^{21} - 16 q^{23} + 4 q^{24} - 12 q^{26} + 24 q^{27} + 4 q^{28} - 8 q^{29} + 36 q^{31} + 4 q^{33} + 24 q^{34} + 256 q^{36} + 8 q^{37} + 20 q^{38} - 20 q^{39} + 24 q^{41} + 28 q^{42} - 40 q^{43} + 20 q^{46} - 16 q^{47} - 16 q^{49} + 36 q^{51} - 4 q^{52} - 12 q^{53} - 8 q^{54} - 4 q^{56} - 72 q^{57} - 12 q^{58} + 12 q^{59} - 20 q^{61} - 24 q^{62} + 68 q^{63} + 256 q^{64} - 8 q^{66} + 12 q^{67} + 12 q^{68} - 8 q^{69} - 56 q^{71} - 8 q^{72} + 48 q^{73} - 36 q^{74} + 16 q^{76} + 4 q^{77} - 48 q^{78} - 20 q^{79} - 112 q^{81} + 24 q^{82} - 8 q^{83} - 52 q^{84} - 4 q^{86} + 60 q^{87} - 8 q^{89} - 60 q^{91} + 32 q^{92} + 92 q^{93} - 8 q^{94} + 4 q^{96} + 96 q^{97} + 32 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(770, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1925, [\chi])\)\(^{\oplus 2}\)