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Properties

Label 3420.2.fc
Level $3420$
Weight $2$
Character orbit 3420.fc
Rep. character $\chi_{3420}(41,\cdot)$
Character field $\Q(\zeta_{18})$
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.fc (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
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 480 3912
Cusp forms 4248 480 3768
Eisenstein series 144 0 144

Trace form

\( 480 q + 12 q^{3} - 12 q^{9} + O(q^{10}) \) \( 480 q + 12 q^{3} - 12 q^{9} + 6 q^{13} + 6 q^{19} + 18 q^{27} + 48 q^{33} - 48 q^{39} + 12 q^{43} - 240 q^{49} - 12 q^{51} - 12 q^{57} - 90 q^{59} + 42 q^{61} - 24 q^{63} + 48 q^{67} - 78 q^{73} - 12 q^{79} + 24 q^{81} - 72 q^{83} - 60 q^{87} + 108 q^{89} + 24 q^{91} - 36 q^{97} + 42 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3420, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1710, [\chi])\)\(^{\oplus 2}\)