Properties

Label 3006.2.d
Level 3006
Weight 2
Character orbit d
Rep. character \(\chi_{3006}(3005,\cdot)\)
Character field \(\Q\)
Dimension 56
Newform subspaces 1
Sturm bound 1008
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 3006 = 2 \cdot 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3006.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 501 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(1008\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3006, [\chi])\).

Total New Old
Modular forms 512 56 456
Cusp forms 496 56 440
Eisenstein series 16 0 16

Trace form

\( 56q - 56q^{4} + O(q^{10}) \) \( 56q - 56q^{4} + 56q^{16} - 16q^{19} + 40q^{25} - 32q^{31} + 56q^{49} + 16q^{61} - 56q^{64} + 16q^{76} + 32q^{85} + 80q^{94} + 96q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3006, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3006.2.d.a \(56\) \(24.003\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(3006, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3006, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(501, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1002, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1503, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database