Properties

Label 3009.2.i
Level 3009
Weight 2
Character orbit i
Rep. character \(\chi_{3009}(353,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 712
Sturm bound 720

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Defining parameters

Level: \( N \) = \( 3009 = 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3009.i (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3009 \)
Character field: \(\Q(i)\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3009, [\chi])\).

Total New Old
Modular forms 728 728 0
Cusp forms 712 712 0
Eisenstein series 16 16 0

Trace form

\( 712q - 720q^{4} - 8q^{7} + O(q^{10}) \) \( 712q - 720q^{4} - 8q^{7} + 704q^{16} - 20q^{21} - 16q^{22} - 18q^{27} + 8q^{28} + 18q^{45} - 24q^{46} + 40q^{48} + 8q^{51} + 34q^{57} + 20q^{63} - 704q^{64} + 20q^{75} - 68q^{78} + 40q^{79} - 64q^{81} + 64q^{84} - 16q^{85} + 192q^{88} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3009, [\chi])\) into irreducible Hecke orbits

The newforms in this space have not yet been added to the LMFDB.