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Properties

Label 3420.2.bt
Level $3420$
Weight $2$
Character orbit 3420.bt
Rep. character $\chi_{3420}(1361,\cdot)$
Character field $\Q(\zeta_{6})$
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.bt (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
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 1464 160 1304
Cusp forms 1416 160 1256
Eisenstein series 48 0 48

Trace form

\( 160 q - 2 q^{7} + 4 q^{9} + O(q^{10}) \) \( 160 q - 2 q^{7} + 4 q^{9} - 6 q^{11} + 12 q^{17} + 2 q^{19} + 80 q^{25} + 18 q^{29} - 12 q^{31} - 18 q^{33} + 2 q^{39} + 6 q^{41} - 16 q^{43} + 4 q^{45} + 36 q^{47} - 78 q^{49} + 6 q^{51} - 24 q^{53} + 16 q^{57} - 36 q^{59} - 14 q^{61} - 24 q^{63} + 60 q^{69} + 8 q^{73} - 6 q^{75} + 36 q^{81} + 6 q^{83} + 36 q^{89} + 12 q^{91} - 32 q^{93} + 12 q^{95} + 76 q^{99} + O(q^{100}) \)

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

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