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Properties

Label 3850.2.w
Level $3850$
Weight $2$
Character orbit 3850.w
Rep. character $\chi_{3850}(1299,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
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.w (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1488 240 1248
Cusp forms 1392 240 1152
Eisenstein series 96 0 96

Trace form

\( 240 q + 120 q^{4} - 16 q^{6} + 112 q^{9} + O(q^{10}) \) \( 240 q + 120 q^{4} - 16 q^{6} + 112 q^{9} - 16 q^{14} - 120 q^{16} + 8 q^{19} + 40 q^{21} - 8 q^{24} + 24 q^{26} + 80 q^{29} + 32 q^{31} + 32 q^{34} + 224 q^{36} - 8 q^{39} + 48 q^{41} + 24 q^{46} + 32 q^{49} - 24 q^{51} - 8 q^{54} - 8 q^{56} - 24 q^{59} + 16 q^{61} - 240 q^{64} + 16 q^{66} - 64 q^{69} + 48 q^{71} - 16 q^{74} + 16 q^{76} + 8 q^{79} - 72 q^{81} + 8 q^{84} - 8 q^{86} - 88 q^{89} + 24 q^{91} + 80 q^{94} + 8 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3850, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1925, [\chi])\)\(^{\oplus 2}\)