Space of modular forms of level 2205, weight 2, and Character 2205.g

• Label: 2205.2.g
• Level: $2205$
• Weight: $2$
• Character orbit: 2205.g
• Rep. character: $\chi_{2205}(2204,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $3$
• Sturm bound: $672$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2205.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(672\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2205, [\chi])\).

	Total	New	Old
Modular forms	368	80	288
Cusp forms	304	80	224
Eisenstein series	64	0	64

Trace form

\( 80 q + 80 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2205, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2205.2.g.a	$2205$	$2$	2205.g	105.g	$2$	$8$	$8$	$17.607$	8.0.\(\cdots\).5	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{4}-\beta _{4}q^{5}+2\beta _{5}q^{11}-\beta _{1}q^{13}+\cdots\)
2205.2.g.b	$2205$	$2$	2205.g	105.g	$2$	$24$	$24$	$17.607$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
2205.2.g.c	$2205$	$2$	2205.g	105.g	$2$	$48$	$48$	$17.607$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2205, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2205, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)