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Properties

Label 3850.2.cx
Level $3850$
Weight $2$
Character orbit 3850.cx
Rep. character $\chi_{3850}(401,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1216$
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.cx (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
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 5952 1216 4736
Cusp forms 5568 1216 4352
Eisenstein series 384 0 384

Trace form

\( 1216 q + 152 q^{4} + 8 q^{6} + 2 q^{7} + 164 q^{9} + O(q^{10}) \) \( 1216 q + 152 q^{4} + 8 q^{6} + 2 q^{7} + 164 q^{9} - 8 q^{13} + 10 q^{14} + 152 q^{16} + 26 q^{17} - 8 q^{18} - 16 q^{21} + 8 q^{22} - 8 q^{23} - 4 q^{24} + 16 q^{26} - 36 q^{27} + 14 q^{28} + 4 q^{29} - 6 q^{31} - 30 q^{33} - 32 q^{34} - 288 q^{36} - 4 q^{38} + 24 q^{39} - 16 q^{41} - 30 q^{42} - 40 q^{43} - 10 q^{44} - 4 q^{46} + 36 q^{47} + 46 q^{49} - 32 q^{51} + 4 q^{52} + 24 q^{53} + 64 q^{54} + 12 q^{56} + 104 q^{57} - 28 q^{58} - 20 q^{59} + 26 q^{61} - 32 q^{62} + 74 q^{63} - 304 q^{64} - 32 q^{66} - 32 q^{67} + 26 q^{68} + 112 q^{69} - 56 q^{71} + 12 q^{72} + 58 q^{73} + 16 q^{74} - 40 q^{76} + 78 q^{77} + 96 q^{78} + 26 q^{79} + 112 q^{81} + 28 q^{82} + 64 q^{83} + 36 q^{84} - 10 q^{86} - 8 q^{87} + 6 q^{88} + 44 q^{89} - 46 q^{91} - 44 q^{92} - 18 q^{93} - 40 q^{94} - 4 q^{96} + 92 q^{97} + 16 q^{98} + 160 q^{99} + O(q^{100}) \)

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

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