Space of modular forms of level 56, weight 5, and Character 56.o

• Label: 56.5.o
• Level: $56$
• Weight: $5$
• Character orbit: 56.o
• Rep. character: $\chi_{56}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $40$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	56.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(40\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(56, [\chi])\).

	Total	New	Old
Modular forms	72	16	56
Cusp forms	56	16	40
Eisenstein series	16	0	16

Trace form

16 * q - 56 * q^7 + 200 * q^9 - 72 * q^11 + 560 * q^15 + 432 * q^17 - 1176 * q^19 - 520 * q^21 + 960 * q^23 + 1008 * q^25 + 1392 * q^29 - 2136 * q^31 - 3432 * q^33 - 4152 * q^35 - 728 * q^37 + 2792 * q^39 - 3904 * q^43 + 5304 * q^45 + 6264 * q^47 + 4064 * q^49 + 5352 * q^51 - 3480 * q^53 + 5872 * q^57 - 2160 * q^59 - 17640 * q^61 + 616 * q^63 - 15528 * q^65 - 4624 * q^67 - 8544 * q^71 + 15240 * q^73 + 53568 * q^75 + 26208 * q^77 + 15520 * q^79 - 8736 * q^81 - 752 * q^85 - 68088 * q^87 - 26280 * q^89 - 34800 * q^91 - 42056 * q^93 + 8688 * q^95 - 23344 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(56, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
56.5.o.a	$56$	$5$	56.o	7.d	$6$	$16$	$8$	$5.789$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓	✓	56.5.o.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-56\)	$2^{38}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}-\beta _{6})q^{3}+\beta _{4}q^{5}+(-5-3\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(56, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(56, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)