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Properties

Label 3420.2.fv
Level $3420$
Weight $2$
Character orbit 3420.fv
Rep. character $\chi_{3420}(251,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $960$
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.fv (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 228 \)
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 4416 960 3456
Cusp forms 4224 960 3264
Eisenstein series 192 0 192

Trace form

\( 960 q - 12 q^{4} + O(q^{10}) \) \( 960 q - 12 q^{4} - 12 q^{10} - 48 q^{13} + 12 q^{16} + 12 q^{34} + 480 q^{49} + 96 q^{52} - 96 q^{61} + 12 q^{64} + 144 q^{70} - 144 q^{73} + 216 q^{76} - 192 q^{85} + 96 q^{88} + 48 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3420, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1140, [\chi])\)\(^{\oplus 2}\)