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Properties

Label 3150.3.bn
Level $3150$
Weight $3$
Character orbit 3150.bn
Rep. character $\chi_{3150}(1499,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $432$
Sturm bound $2160$

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Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3150.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(2160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3150, [\chi])\).

Total New Old
Modular forms 2928 432 2496
Cusp forms 2832 432 2400
Eisenstein series 96 0 96

Trace form

\( 432 q - 432 q^{4} + 24 q^{9} + O(q^{10}) \) \( 432 q - 432 q^{4} + 24 q^{9} + 72 q^{11} - 864 q^{16} - 56 q^{21} - 120 q^{31} - 144 q^{36} - 200 q^{39} - 288 q^{41} + 1512 q^{49} + 256 q^{51} + 432 q^{54} + 576 q^{59} + 3456 q^{64} - 32 q^{66} + 712 q^{69} + 576 q^{74} + 24 q^{79} - 1080 q^{81} + 224 q^{84} + 432 q^{86} + 336 q^{91} + 1392 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)