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Properties

Label 3150.3.dc
Level $3150$
Weight $3$
Character orbit 3150.dc
Rep. character $\chi_{3150}(431,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1280$
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.dc (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(2160\)

Dimensions

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

Total New Old
Modular forms 11648 1280 10368
Cusp forms 11392 1280 10112
Eisenstein series 256 0 256

Trace form

\( 1280 q - 320 q^{4} - 16 q^{7} + O(q^{10}) \) \( 1280 q - 320 q^{4} - 16 q^{7} - 16 q^{10} + 640 q^{16} - 224 q^{22} + 40 q^{25} - 48 q^{28} + 120 q^{31} - 128 q^{37} + 32 q^{40} + 32 q^{43} - 240 q^{46} - 16 q^{55} - 32 q^{58} + 2560 q^{64} + 64 q^{67} - 480 q^{70} + 144 q^{73} - 80 q^{79} - 1024 q^{82} - 1264 q^{85} + 256 q^{88} + 680 q^{91} - 320 q^{94} - 1296 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)