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Properties

Label 3420.2.hg
Level $3420$
Weight $2$
Character orbit 3420.hg
Rep. character $\chi_{3420}(193,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1440$
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.hg (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 855 \)
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 8784 1440 7344
Cusp forms 8496 1440 7056
Eisenstein series 288 0 288

Trace form

\( 1440 q + O(q^{10}) \) \( 1440 q - 36 q^{15} + 18 q^{17} + 24 q^{23} + 36 q^{33} - 36 q^{35} - 36 q^{45} + 96 q^{51} - 36 q^{57} + 36 q^{63} + 72 q^{81} - 48 q^{87} + 12 q^{93} + O(q^{100}) \)

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

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