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Properties

Label 3520.2.ct
Level $3520$
Weight $2$
Character orbit 3520.ct
Rep. character $\chi_{3520}(449,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $560$
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.ct (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 2400 592 1808
Cusp forms 2208 560 1648
Eisenstein series 192 32 160

Trace form

\( 560 q + 6 q^{5} + 120 q^{9} + O(q^{10}) \) \( 560 q + 6 q^{5} + 120 q^{9} + 56 q^{21} - 6 q^{25} + 12 q^{29} - 12 q^{41} + 104 q^{45} + 104 q^{49} + 12 q^{61} - 36 q^{65} + 24 q^{69} - 144 q^{81} + 74 q^{85} - 32 q^{89} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1760, [\chi])\)\(^{\oplus 2}\)