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Properties

Label 3420.2.dt
Level $3420$
Weight $2$
Character orbit 3420.dt
Rep. character $\chi_{3420}(493,\cdot)$
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.dt (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

\( 480 q + O(q^{10}) \) \( 480 q - 24 q^{17} + 16 q^{23} + 48 q^{35} - 20 q^{45} - 20 q^{47} + 10 q^{57} + 8 q^{63} - 48 q^{81} - 152 q^{87} + 152 q^{93} - 12 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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