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Properties

Label 3850.2.cq
Level $3850$
Weight $2$
Character orbit 3850.cq
Rep. character $\chi_{3850}(243,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $480$
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.cq (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 2976 480 2496
Cusp forms 2784 480 2304
Eisenstein series 192 0 192

Trace form

\( 480 q + O(q^{10}) \) \( 480 q + 240 q^{16} - 72 q^{17} - 16 q^{18} - 32 q^{21} + 96 q^{31} - 512 q^{36} + 48 q^{38} + 48 q^{42} + 64 q^{43} - 48 q^{46} - 16 q^{53} + 16 q^{56} - 80 q^{57} - 32 q^{58} + 192 q^{61} - 136 q^{63} + 16 q^{67} - 72 q^{68} + 128 q^{71} - 16 q^{72} + 96 q^{73} + 32 q^{78} + 272 q^{81} - 48 q^{82} + 48 q^{86} - 72 q^{87} - 48 q^{91} + 8 q^{93} + 48 q^{96} + 112 q^{98} + O(q^{100}) \)

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

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