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Properties

Label 3150.2.cu
Level $3150$
Weight $2$
Character orbit 3150.cu
Rep. character $\chi_{3150}(433,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $800$
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.cu (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 5888 800 5088
Cusp forms 5632 800 4832
Eisenstein series 256 0 256

Trace form

\( 800 q + O(q^{10}) \) \( 800 q + 200 q^{16} + 24 q^{22} - 16 q^{23} - 16 q^{25} - 20 q^{28} - 40 q^{29} - 20 q^{35} - 16 q^{37} - 80 q^{43} + 32 q^{50} + 32 q^{53} - 24 q^{65} + 48 q^{67} + 80 q^{70} + 144 q^{77} - 32 q^{85} + 16 q^{88} + 24 q^{92} + 24 q^{95} + 16 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)