Properties

Label 3420.2.eo
Level $3420$
Weight $2$
Character orbit 3420.eo
Rep. character $\chi_{3420}(353,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $480$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3420.eo (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 855 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3420, [\chi])\).

Total New Old
Modular forms 2928 480 2448
Cusp forms 2832 480 2352
Eisenstein series 96 0 96

Trace form

\( 480 q + O(q^{10}) \) \( 480 q + 12 q^{15} + 18 q^{17} - 24 q^{23} + 6 q^{27} - 24 q^{33} - 8 q^{45} - 32 q^{51} + 28 q^{57} - 56 q^{63} + 24 q^{65} - 6 q^{75} - 96 q^{77} + 24 q^{81} + 8 q^{87} - 20 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3420, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3420, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3420, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1710, [\chi])\)\(^{\oplus 2}\)