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Properties

Label 3150.2.ee
Level $3150$
Weight $2$
Character orbit 3150.ee
Rep. character $\chi_{3150}(23,\cdot)$
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.ee (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

\( 3840 q + O(q^{10}) \) \( 3840 q - 12 q^{15} + 960 q^{16} + 36 q^{17} + 8 q^{18} - 24 q^{23} - 36 q^{27} + 12 q^{30} - 40 q^{33} - 80 q^{39} + 4 q^{42} - 88 q^{45} + 48 q^{50} - 32 q^{57} + 12 q^{58} + 16 q^{60} - 48 q^{63} - 144 q^{68} + 140 q^{69} - 8 q^{72} + 152 q^{75} + 384 q^{77} + 16 q^{78} - 60 q^{84} - 76 q^{87} - 300 q^{89} + 80 q^{90} + 24 q^{92} + O(q^{100}) \)

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

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