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Properties

Label 3420.2.r
Level $3420$
Weight $2$
Character orbit 3420.r
Rep. character $\chi_{3420}(1141,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $144$
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.r (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
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 144 1320
Cusp forms 1416 144 1272
Eisenstein series 48 0 48

Trace form

\( 144 q - 4 q^{5} - 12 q^{9} + O(q^{10}) \) \( 144 q - 4 q^{5} - 12 q^{9} - 4 q^{11} + 4 q^{15} + 32 q^{17} + 40 q^{21} - 12 q^{23} - 72 q^{25} + 12 q^{27} + 12 q^{29} - 40 q^{33} + 16 q^{35} + 8 q^{39} + 28 q^{41} + 8 q^{45} + 12 q^{47} - 60 q^{49} - 28 q^{51} - 32 q^{53} + 12 q^{61} + 4 q^{63} - 4 q^{65} + 36 q^{69} - 80 q^{71} - 28 q^{77} - 12 q^{79} - 76 q^{81} - 32 q^{83} - 12 q^{85} - 40 q^{87} + 32 q^{89} + 24 q^{91} - 68 q^{93} + 52 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3420, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 2}\)