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Properties

Label 3850.2.p
Level $3850$
Weight $2$
Character orbit 3850.p
Rep. character $\chi_{3850}(1401,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $456$
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.p (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
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 2976 456 2520
Cusp forms 2784 456 2328
Eisenstein series 192 0 192

Trace form

\( 456 q + 2 q^{2} - 114 q^{4} - 6 q^{6} + 2 q^{8} - 102 q^{9} + O(q^{10}) \) \( 456 q + 2 q^{2} - 114 q^{4} - 6 q^{6} + 2 q^{8} - 102 q^{9} - 18 q^{11} + 20 q^{12} - 28 q^{13} - 114 q^{16} + 12 q^{17} - 34 q^{19} + 8 q^{21} + 2 q^{22} + 8 q^{23} - 6 q^{24} + 4 q^{26} - 6 q^{27} - 56 q^{29} - 40 q^{31} - 8 q^{32} - 6 q^{33} - 4 q^{34} - 132 q^{36} - 44 q^{37} + 44 q^{38} - 48 q^{39} + 12 q^{41} + 76 q^{43} - 8 q^{44} + 8 q^{46} - 4 q^{47} - 114 q^{49} + 58 q^{51} + 32 q^{52} + 40 q^{53} + 40 q^{54} + 70 q^{57} + 20 q^{58} - 38 q^{59} - 40 q^{61} + 24 q^{62} - 114 q^{64} + 52 q^{66} + 4 q^{67} + 12 q^{68} + 152 q^{69} + 64 q^{71} + 10 q^{72} - 20 q^{73} - 52 q^{74} - 4 q^{76} - 8 q^{77} - 96 q^{78} + 8 q^{79} - 116 q^{81} - 18 q^{82} - 98 q^{83} + 8 q^{84} - 82 q^{86} + 40 q^{87} + 2 q^{88} - 228 q^{89} + 36 q^{91} + 8 q^{92} - 28 q^{93} - 32 q^{94} + 4 q^{96} - 118 q^{97} - 8 q^{98} + 130 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(770, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1925, [\chi])\)\(^{\oplus 2}\)