Space of modular forms of level 280, weight 10, and Character 280.g

• Label: 280.10.g
• Level: $280$
• Weight: $10$
• Character orbit: 280.g
• Rep. character: $\chi_{280}(169,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $480$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	280.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(480\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(280, [\chi])\).

	Total	New	Old
Modular forms	440	80	360
Cusp forms	424	80	344
Eisenstein series	16	0	16

Trace form

80 * q - 2276 * q^5 - 498636 * q^9 + 175692 * q^11 + 26384 * q^15 - 777924 * q^21 - 1197084 * q^25 + 18992396 * q^29 - 408888 * q^31 - 39274996 * q^39 + 29717056 * q^41 + 32943060 * q^45 - 461184080 * q^49 + 153434532 * q^51 + 110984624 * q^55 + 281706024 * q^59 + 533840920 * q^61 + 388142856 * q^65 - 390996328 * q^69 - 664358328 * q^71 + 60320128 * q^75 + 318455252 * q^79 + 3031909672 * q^81 + 64190420 * q^85 + 1165008312 * q^89 + 822899532 * q^91 - 441698868 * q^95 - 6754749704 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(280, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
280.10.g.a	$280$	$10$	280.g	5.b	$2$	$38$	$38$	$144.210$		None		✓			280.10.g.a	$2$	$0$	\(0\)	\(0\)	\(-3136\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
280.10.g.b	$280$	$10$	280.g	5.b	$2$	$42$	$42$	$144.210$		None		✓	✓		280.10.g.b	$2$	$0$	\(0\)	\(0\)	\(860\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{10}^{\mathrm{old}}(280, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(280, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)