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Properties

Label 3420.2.gm
Level $3420$
Weight $2$
Character orbit 3420.gm
Rep. character $\chi_{3420}(283,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $8544$
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.gm (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3420 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 8736 8736 0
Cusp forms 8544 8544 0
Eisenstein series 192 192 0

Trace form

\( 8544 q - 6 q^{2} - 12 q^{5} - 24 q^{6} - 12 q^{8} + O(q^{10}) \) \( 8544 q - 6 q^{2} - 12 q^{5} - 24 q^{6} - 12 q^{8} - 24 q^{10} - 6 q^{12} - 12 q^{13} - 12 q^{16} - 48 q^{17} - 24 q^{18} - 12 q^{20} - 48 q^{21} + 42 q^{22} - 12 q^{25} + 24 q^{26} - 48 q^{28} - 6 q^{30} - 6 q^{32} + 48 q^{33} - 24 q^{36} - 96 q^{37} - 6 q^{38} - 6 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 24 q^{46} + 30 q^{48} - 12 q^{50} - 6 q^{52} - 48 q^{53} - 24 q^{56} - 24 q^{57} - 12 q^{58} - 12 q^{60} - 24 q^{61} - 12 q^{62} - 24 q^{65} + 120 q^{66} + 6 q^{68} - 6 q^{70} - 60 q^{72} - 48 q^{73} - 12 q^{76} + 144 q^{77} - 18 q^{78} - 24 q^{80} - 48 q^{81} - 24 q^{82} - 12 q^{85} + 96 q^{86} + 102 q^{88} - 12 q^{90} - 6 q^{92} + 48 q^{93} - 12 q^{97} - 54 q^{98} + O(q^{100}) \)

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.