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Properties

Label 3150.2.db
Level $3150$
Weight $2$
Character orbit 3150.db
Rep. character $\chi_{3150}(89,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $640$
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.db (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 5888 640 5248
Cusp forms 5632 640 4992
Eisenstein series 256 0 256

Trace form

\( 640 q + 80 q^{4} + O(q^{10}) \) \( 640 q + 80 q^{4} - 12 q^{10} + 80 q^{16} - 80 q^{22} + 12 q^{25} - 20 q^{28} + 36 q^{31} + 12 q^{40} - 24 q^{46} + 8 q^{49} - 160 q^{64} - 12 q^{70} - 240 q^{73} - 8 q^{79} - 48 q^{85} + 20 q^{88} + 104 q^{91} + 96 q^{94} + O(q^{100}) \)

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

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