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Properties

Label 3520.2.du
Level $3520$
Weight $2$
Character orbit 3520.du
Rep. character $\chi_{3520}(383,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1120$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3520.du (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 220 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3520, [\chi])\).

Total New Old
Modular forms 4800 1184 3616
Cusp forms 4416 1120 3296
Eisenstein series 384 64 320

Trace form

\( 1120 q + 12 q^{5} + O(q^{10}) \) \( 1120 q + 12 q^{5} + 12 q^{13} - 12 q^{17} + 64 q^{21} - 12 q^{25} - 28 q^{33} + 12 q^{37} - 24 q^{41} + 72 q^{45} - 36 q^{53} + 12 q^{57} + 24 q^{61} - 32 q^{65} - 12 q^{73} + 92 q^{77} + 192 q^{81} + 108 q^{85} + 84 q^{93} + 52 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3520, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1760, [\chi])\)\(^{\oplus 2}\)