Properties

Label 3520.2.dw
Level $3520$
Weight $2$
Character orbit 3520.dw
Rep. character $\chi_{3520}(223,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1152$
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.dw (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 440 \)
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 1152 3648
Cusp forms 4416 1152 3264
Eisenstein series 384 0 384

Trace form

\( 1152 q + O(q^{10}) \) \( 1152 q + 288 q^{81} + 192 q^{97} + O(q^{100}) \)

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

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