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Properties

Label 3850.2.cr
Level $3850$
Weight $2$
Character orbit 3850.cr
Rep. character $\chi_{3850}(1143,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $576$
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.cr (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
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 576 2400
Cusp forms 2784 576 2208
Eisenstein series 192 0 192

Trace form

\( 576 q + O(q^{10}) \) \( 576 q - 8 q^{11} + 288 q^{16} - 24 q^{22} + 8 q^{23} + 16 q^{26} + 16 q^{33} - 640 q^{36} + 40 q^{37} + 40 q^{42} + 40 q^{47} - 40 q^{53} - 32 q^{56} - 32 q^{58} + 48 q^{67} - 64 q^{71} + 72 q^{77} + 352 q^{81} - 16 q^{82} + 12 q^{88} + 224 q^{91} + 16 q^{92} - 80 q^{93} + 64 q^{97} + O(q^{100}) \)

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

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