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

• Label: 294.3.h
• Level: $294$
• Weight: $3$
• Character orbit: 294.h
• Rep. character: $\chi_{294}(263,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $52$
• Newform subspaces: $8$
• Sturm bound: $168$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	294.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
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	256	52	204
Cusp forms	192	52	140
Eisenstein series	64	0	64

Trace form

\( 52 q + 52 q^{4} - 8 q^{6} + O(q^{10}) \)

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.h.a	$294$	$3$	294.h	21.h	$6$	$4$	$2$	$8.011$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-2\beta _{1}-\beta _{2}+2\beta _{3})q^{3}+\cdots\)
294.3.h.b	$294$	$3$	294.h	21.h	$6$	$4$	$2$	$8.011$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-2\beta _{1}-\beta _{2}+2\beta _{3})q^{3}+\cdots\)
294.3.h.c	$294$	$3$	294.h	21.h	$6$	$4$	$2$	$8.011$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{2}-2\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
294.3.h.d	$294$	$3$	294.h	21.h	$6$	$8$	$4$	$8.011$	8.0.\(\cdots\).5	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{4}-\beta _{5}-\beta _{6})q^{3}+\cdots\)
294.3.h.e	$294$	$3$	294.h	21.h	$6$	$8$	$4$	$8.011$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{24}^{5}q^{2}+(\zeta_{24}-2\zeta_{24}^{4}+2\zeta_{24}^{7})q^{3}+\cdots\)
294.3.h.f	$294$	$3$	294.h	21.h	$6$	$8$	$4$	$8.011$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{24}^{5}q^{2}-3\zeta_{24}q^{3}+(2-2\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
294.3.h.g	$294$	$3$	294.h	21.h	$6$	$8$	$4$	$8.011$	8.0.\(\cdots\).5	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{4}-\beta _{6})q^{2}+(\beta _{4}-\beta _{5})q^{3}+2\beta _{2}q^{4}+\cdots\)
294.3.h.h	$294$	$3$	294.h	21.h	$6$	$8$	$4$	$8.011$	8.0.4857532416.2	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)

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

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