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Properties

Label 3150.2.cb
Level $3150$
Weight $2$
Character orbit 3150.cb
Rep. character $\chi_{3150}(443,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $576$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3150.cb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 2976 576 2400
Cusp forms 2784 576 2208
Eisenstein series 192 0 192

Trace form

\( 576 q - 16 q^{6} + O(q^{10}) \) \( 576 q - 16 q^{6} + 288 q^{16} - 36 q^{17} - 16 q^{18} + 24 q^{21} - 36 q^{27} + 20 q^{33} - 24 q^{41} + 4 q^{42} + 24 q^{46} + 48 q^{51} + 48 q^{57} - 24 q^{58} - 24 q^{61} + 28 q^{63} - 8 q^{72} + 48 q^{77} + 16 q^{78} - 8 q^{81} - 40 q^{87} + 24 q^{92} + 12 q^{93} - 8 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)