Space of modular forms of level 605, weight 2, and Character 605.u

• Label: 605.2.u
• Level: $605$
• Weight: $2$
• Character orbit: 605.u
• Rep. character: $\chi_{605}(4,\cdot)$
• Character field: $\Q(\zeta_{110})$
• Dimension: $2560$
• Newform subspaces: $1$
• Sturm bound: $132$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.u (of order \(110\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 605 \)
Character field:			\(\Q(\zeta_{110})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(132\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(605, [\chi])\).

	Total	New	Old
Modular forms	2720	2720	0
Cusp forms	2560	2560	0
Eisenstein series	160	160	0

Trace form

\( 2560 q - 144 q^{4} - 43 q^{5} - 114 q^{6} + 534 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(605, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
605.2.u.a	$605$	$2$	605.u	605.u	$110$	$2560$	$64$	$4.831$		None		$4$	$0$	\(0\)	\(0\)	\(-43\)	\(0\)		$\mathrm{SU}(2)[C_{110}]$