Properties

Label 1008.2.ch
Level 1008
Weight 2
Character orbit ch
Rep. character \(\chi_{1008}(239,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 72
Newform subspaces 3
Sturm bound 384
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1008.ch (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(384\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1008, [\chi])\).

Total New Old
Modular forms 408 72 336
Cusp forms 360 72 288
Eisenstein series 48 0 48

Trace form

\( 72q - 12q^{9} + O(q^{10}) \) \( 72q - 12q^{9} + 36q^{25} + 36q^{33} + 36q^{41} + 24q^{45} + 36q^{49} - 36q^{57} - 72q^{65} - 24q^{69} + 72q^{73} - 36q^{81} + 48q^{93} + 36q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1008.2.ch.a \(24\) \(8.049\) None \(0\) \(-6\) \(6\) \(0\)
1008.2.ch.b \(24\) \(8.049\) None \(0\) \(0\) \(-12\) \(0\)
1008.2.ch.c \(24\) \(8.049\) None \(0\) \(6\) \(6\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database