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Properties

Label 3120.2.hw
Level $3120$
Weight $2$
Character orbit 3120.hw
Rep. character $\chi_{3120}(17,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $656$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3120.hw (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 195 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3120, [\chi])\).

Total New Old
Modular forms 2784 688 2096
Cusp forms 2592 656 1936
Eisenstein series 192 32 160

Trace form

\( 656 q + 2 q^{3} + 12 q^{7} + O(q^{10}) \) \( 656 q + 2 q^{3} + 12 q^{7} - 8 q^{13} + 6 q^{15} - 16 q^{25} + 8 q^{27} - 6 q^{33} + 36 q^{37} - 12 q^{43} + 24 q^{45} - 32 q^{51} - 8 q^{61} + 6 q^{63} + 84 q^{67} + 2 q^{75} - 4 q^{81} - 12 q^{85} - 10 q^{87} - 80 q^{91} + 12 q^{93} - 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3120, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1560, [\chi])\)\(^{\oplus 2}\)