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

• Label: 345.2.c
• Level: $345$
• Weight: $2$
• Character orbit: 345.c
• Rep. character: $\chi_{345}(206,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 69 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(11\)

Dimensions

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

	Total	New	Old
Modular forms	52	32	20
Cusp forms	44	32	12
Eisenstein series	8	0	8

Trace form

32 * q - 28 * q^4 + 2 * q^6 - 4 * q^9 + 6 * q^12 - 4 * q^16 - 22 * q^18 + 32 * q^25 - 12 * q^27 - 16 * q^31 + 58 * q^36 + 8 * q^39 - 12 * q^46 - 46 * q^48 - 64 * q^49 - 4 * q^52 + 52 * q^54 - 16 * q^55 - 84 * q^58 + 104 * q^64 - 20 * q^69 - 24 * q^70 + 56 * q^72 + 24 * q^73 + 98 * q^78 - 12 * q^81 - 52 * q^82 - 16 * q^85 - 32 * q^87 + 20 * q^93 + 60 * q^94 - 26 * q^96

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
345.2.c.a	$345$	$2$	345.c	69.c	$2$	$16$	$16$	$2.755$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			345.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots\)
345.2.c.b	$345$	$2$	345.c	69.c	$2$	$16$	$16$	$2.755$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			345.2.c.a	$2$	$0$	\(0\)	\(0\)	\(16\)	\(0\)	$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-1+\beta _{2})q^{4}+q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(345, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(345, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)