Space of modular forms of level 345, weight 2, and Character 345.i

• Label: 345.2.i
• Level: $345$
• Weight: $2$
• Character orbit: 345.i
• Rep. character: $\chi_{345}(47,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $88$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(345, [\chi])\).

	Total	New	Old
Modular forms	104	88	16
Cusp forms	88	88	0
Eisenstein series	16	0	16

Trace form

\( 88 q - 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(345, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
345.2.i.a	$345$	$2$	345.i	15.e	$4$	$4$	$2$	$2.755$	\(\Q(\zeta_{8})\)	None		$2$	$1$	\(-4\)	\(-4\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\zeta_{8}^{2})q^{2}+(-1+\zeta_{8}+\zeta_{8}^{3})q^{3}+\cdots\)
345.2.i.b	$345$	$2$	345.i	15.e	$4$	$4$	$2$	$2.755$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(4\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\zeta_{8}^{2})q^{2}+(-\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
345.2.i.c	$345$	$2$	345.i	15.e	$4$	$80$	$40$	$2.755$		None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{4}]$