Space of modular forms of level 1003, weight 6, and Character 1003.e

• Label: 1003.6.e
• Level: $1003$
• Weight: $6$
• Character orbit: 1003.e
• Rep. character: $\chi_{1003}(591,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $872$
• Sturm bound: $540$

Defining parameters

Level:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1003.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1003, [\chi])\).

	Total	New	Old
Modular forms	904	872	32
Cusp forms	896	872	24
Eisenstein series	8	0	8

Trace form

\( 872 q - 14016 q^{4} + 76 q^{5} - 360 q^{6} + 236 q^{7} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(1003, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(1003, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1003, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)