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Properties

Label 3150.3.bw
Level $3150$
Weight $3$
Character orbit 3150.bw
Rep. character $\chi_{3150}(71,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $480$
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.bw (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(2160\)

Dimensions

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

Total New Old
Modular forms 5824 480 5344
Cusp forms 5696 480 5216
Eisenstein series 128 0 128

Trace form

\( 480 q + 240 q^{4} + O(q^{10}) \) \( 480 q + 240 q^{4} - 8 q^{10} + 64 q^{13} - 480 q^{16} + 240 q^{19} + 48 q^{22} - 448 q^{25} - 120 q^{34} - 104 q^{37} + 16 q^{40} - 352 q^{43} - 240 q^{46} + 3360 q^{49} - 128 q^{52} + 304 q^{55} - 112 q^{58} + 560 q^{61} + 960 q^{64} - 928 q^{67} - 112 q^{70} + 32 q^{73} + 320 q^{76} + 480 q^{79} - 16 q^{82} + 1712 q^{85} + 64 q^{88} + 768 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)