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Properties

Label 3420.2.q
Level $3420$
Weight $2$
Character orbit 3420.q
Rep. character $\chi_{3420}(121,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $160$
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1464 160 1304
Cusp forms 1416 160 1256
Eisenstein series 48 0 48

Trace form

\( 160 q - 2 q^{3} + 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( 160 q - 2 q^{3} + 2 q^{7} - 2 q^{9} + 2 q^{11} + 2 q^{13} - 4 q^{17} - 2 q^{19} + 160 q^{25} - 20 q^{27} + 12 q^{29} - 4 q^{31} - 10 q^{33} - 4 q^{37} + 10 q^{39} - 20 q^{41} - 16 q^{43} + 4 q^{45} - 78 q^{49} + 32 q^{51} + 16 q^{53} - 14 q^{57} - 28 q^{61} + 60 q^{63} + 16 q^{65} + 20 q^{67} - 60 q^{69} + 16 q^{71} + 20 q^{73} - 2 q^{75} + 20 q^{77} + 2 q^{79} - 30 q^{81} - 2 q^{83} - 16 q^{87} + 20 q^{89} - 32 q^{91} - 24 q^{93} - 8 q^{95} + 2 q^{97} + 16 q^{99} + O(q^{100}) \)

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

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