Space of modular forms of level 294, weight 3, and Character 294.b

• Label: 294.3.b
• Level: $294$
• Weight: $3$
• Character orbit: 294.b
• Rep. character: $\chi_{294}(197,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $9$
• Sturm bound: $168$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	294.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(168\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(294, [\chi])\).

	Total	New	Old
Modular forms	128	28	100
Cusp forms	96	28	68
Eisenstein series	32	0	32

Trace form

\( 28 q - 56 q^{4} + 8 q^{6} - 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(294, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
294.3.b.a	$294$	$3$	294.b	3.b	$2$	$2$	$2$	$8.011$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(-1-2\beta )q^{3}-2q^{4}+\beta q^{5}+\cdots\)
294.3.b.b	$294$	$3$	294.b	3.b	$2$	$2$	$2$	$8.011$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(-1-2\beta )q^{3}-2q^{4}-6\beta q^{5}+\cdots\)
294.3.b.c	$294$	$3$	294.b	3.b	$2$	$2$	$2$	$8.011$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(1+2\beta )q^{3}-2q^{4}+6\beta q^{5}+\cdots\)
294.3.b.d	$294$	$3$	294.b	3.b	$2$	$2$	$2$	$8.011$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+(1+2\beta )q^{3}-2q^{4}-\beta q^{5}+\cdots\)
294.3.b.e	$294$	$3$	294.b	3.b	$2$	$4$	$4$	$8.011$	\(\Q(\sqrt{-2}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}-2q^{4}+\cdots\)
294.3.b.f	$294$	$3$	294.b	3.b	$2$	$4$	$4$	$8.011$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{2}+3\zeta_{8}q^{3}-2q^{4}-8\zeta_{8}q^{5}+\cdots\)
294.3.b.g	$294$	$3$	294.b	3.b	$2$	$4$	$4$	$8.011$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+2\zeta_{8}^{3})q^{3}-2q^{4}+\cdots\)
294.3.b.h	$294$	$3$	294.b	3.b	$2$	$4$	$4$	$8.011$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}-2q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
294.3.b.i	$294$	$3$	294.b	3.b	$2$	$4$	$4$	$8.011$	\(\Q(\sqrt{-2}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}-2q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(294, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(294, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)