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Properties

Label 3420.2.et
Level $3420$
Weight $2$
Character orbit 3420.et
Rep. character $\chi_{3420}(169,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $720$
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.et (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 855 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 4392 720 3672
Cusp forms 4248 720 3528
Eisenstein series 144 0 144

Trace form

\( 720 q + O(q^{10}) \) \( 720 q + 21 q^{15} + 18 q^{35} + 12 q^{39} - 27 q^{45} - 720 q^{49} - 54 q^{51} + 12 q^{59} - 30 q^{65} - 36 q^{71} - 60 q^{81} + 60 q^{95} + 60 q^{99} + O(q^{100}) \)

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

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