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

• Label: 345.2.b
• Level: $345$
• Weight: $2$
• Character orbit: 345.b
• Rep. character: $\chi_{345}(139,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	52	24	28
Cusp forms	44	24	20
Eisenstein series	8	0	8

Trace form

24 * q - 28 * q^4 + 4 * q^5 + 4 * q^6 - 24 * q^9 - 8 * q^14 - 4 * q^15 + 36 * q^16 + 8 * q^19 + 4 * q^20 - 8 * q^21 - 12 * q^24 - 32 * q^26 + 12 * q^29 - 8 * q^30 + 20 * q^31 + 32 * q^34 - 36 * q^35 + 28 * q^36 - 8 * q^39 + 24 * q^40 + 28 * q^41 - 40 * q^44 - 4 * q^45 + 8 * q^46 - 52 * q^49 + 48 * q^50 - 4 * q^54 + 12 * q^59 + 36 * q^60 - 100 * q^64 + 16 * q^65 - 8 * q^66 - 8 * q^69 + 64 * q^70 - 4 * q^71 - 88 * q^74 + 8 * q^75 - 32 * q^76 + 40 * q^79 + 76 * q^80 + 24 * q^81 + 56 * q^84 + 12 * q^85 - 48 * q^86 - 48 * q^89 - 48 * q^91 - 80 * q^94 + 8 * q^95 + 28 * 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.b.a	$345$	$2$	345.b	5.b	$2$	$2$	$2$	$2.755$	\(\Q(\sqrt{-1}) \)	None		✓			345.2.b.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}+q^{4}+(2 i+1)q^{5}+\cdots\)
345.2.b.b	$345$	$2$	345.b	5.b	$2$	$2$	$2$	$2.755$	\(\Q(\sqrt{-1}) \)	None		✓			345.2.b.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}+q^{4}+(-i+2)q^{5}+\cdots\)
345.2.b.c	$345$	$2$	345.b	5.b	$2$	$6$	$6$	$2.755$	6.0.350464.1	None		✓			345.2.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
345.2.b.d	$345$	$2$	345.b	5.b	$2$	$14$	$14$	$2.755$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓	✓		345.2.b.d	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-\beta _{2}q^{3}+(-2-\beta _{8}+\beta _{9}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(345, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)