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Properties

Label 3420.2.ef
Level $3420$
Weight $2$
Character orbit 3420.ef
Rep. character $\chi_{3420}(77,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $432$
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.ef (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
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 432 2496
Cusp forms 2832 432 2400
Eisenstein series 96 0 96

Trace form

\( 432 q + 4 q^{3} + O(q^{10}) \) \( 432 q + 4 q^{3} - 24 q^{11} - 8 q^{15} - 8 q^{21} - 12 q^{25} + 40 q^{27} + 28 q^{33} - 24 q^{37} + 24 q^{41} + 24 q^{47} + 24 q^{51} - 24 q^{55} + 24 q^{61} - 76 q^{63} - 12 q^{67} - 40 q^{75} - 64 q^{81} - 120 q^{83} + 48 q^{85} + 48 q^{91} - 16 q^{93} + 36 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3420, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)