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Properties

Label 3150.2.ei
Level $3150$
Weight $2$
Character orbit 3150.ei
Rep. character $\chi_{3150}(13,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3840$
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.ei (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 11648 3840 7808
Cusp forms 11392 3840 7552
Eisenstein series 256 0 256

Trace form

\( 3840 q + O(q^{10}) \) \( 3840 q - 24 q^{15} - 480 q^{16} + 8 q^{18} - 8 q^{23} - 48 q^{30} + 24 q^{35} - 40 q^{39} + 44 q^{42} - 32 q^{50} + 160 q^{53} + 72 q^{57} - 24 q^{58} - 8 q^{60} + 148 q^{63} + 8 q^{65} - 16 q^{72} - 144 q^{77} + 16 q^{78} + 60 q^{84} - 8 q^{92} + 120 q^{93} + 128 q^{95} + 48 q^{98} + O(q^{100}) \)

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

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