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Properties

Label 3150.2.s
Level $3150$
Weight $2$
Character orbit 3150.s
Rep. character $\chi_{3150}(299,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $288$
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.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1488 288 1200
Cusp forms 1392 288 1104
Eisenstein series 96 0 96

Trace form

\( 288 q - 144 q^{4} - 12 q^{9} + O(q^{10}) \) \( 288 q - 144 q^{4} - 12 q^{9} - 12 q^{14} - 144 q^{16} - 8 q^{21} - 12 q^{24} + 12 q^{29} - 12 q^{39} - 12 q^{41} + 24 q^{44} - 12 q^{46} + 24 q^{49} + 20 q^{51} + 36 q^{61} + 288 q^{64} + 48 q^{66} - 84 q^{69} - 12 q^{79} + 76 q^{81} + 28 q^{84} - 72 q^{89} + 12 q^{96} + 72 q^{99} + O(q^{100}) \)

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

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