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Properties

Label 3420.2.bg
Level $3420$
Weight $2$
Character orbit 3420.bg
Rep. character $\chi_{3420}(1151,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
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.bg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 228 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1472 320 1152
Cusp forms 1408 320 1088
Eisenstein series 64 0 64

Trace form

\( 320 q + 4 q^{4} + O(q^{10}) \) \( 320 q + 4 q^{4} + 4 q^{10} + 16 q^{13} - 4 q^{16} + 160 q^{25} + 4 q^{34} + 32 q^{37} + 8 q^{40} + 64 q^{46} - 224 q^{49} - 32 q^{52} - 64 q^{58} - 80 q^{61} - 32 q^{64} + 24 q^{70} + 48 q^{73} + 96 q^{76} - 80 q^{82} - 32 q^{85} + 208 q^{88} + 72 q^{94} - 96 q^{97} + O(q^{100}) \)

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

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