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Properties

Label 3850.2.fg
Level $3850$
Weight $2$
Character orbit 3850.fg
Rep. character $\chi_{3850}(299,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1152$
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.fg (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 5952 1152 4800
Cusp forms 5568 1152 4416
Eisenstein series 384 0 384

Trace form

\( 1152 q + 144 q^{4} + 168 q^{9} + O(q^{10}) \) \( 1152 q + 144 q^{4} + 168 q^{9} + 8 q^{11} - 12 q^{14} + 144 q^{16} - 24 q^{26} - 36 q^{31} - 256 q^{36} + 40 q^{39} + 28 q^{44} - 36 q^{49} + 120 q^{51} - 16 q^{56} + 60 q^{61} - 288 q^{64} + 192 q^{66} + 64 q^{71} + 216 q^{81} + 36 q^{86} + 120 q^{89} - 60 q^{91} - 300 q^{94} + 112 q^{99} + O(q^{100}) \)

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

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