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Properties

Label 3150.2.bz
Level $3150$
Weight $2$
Character orbit 3150.bz
Rep. character $\chi_{3150}(881,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $320$
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.bz (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 2944 320 2624
Cusp forms 2816 320 2496
Eisenstein series 128 0 128

Trace form

\( 320 q + 80 q^{4} + 8 q^{7} + O(q^{10}) \) \( 320 q + 80 q^{4} + 8 q^{7} - 80 q^{16} - 40 q^{22} - 16 q^{25} + 12 q^{28} + 16 q^{37} + 32 q^{43} - 24 q^{46} - 8 q^{49} + 16 q^{58} + 80 q^{64} - 64 q^{67} + 60 q^{70} - 16 q^{79} + 80 q^{85} - 40 q^{88} + 104 q^{91} + O(q^{100}) \)

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

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