Space of modular forms of level 10, weight 8, and Character 10.b

• Label: 10.8.b
• Level: $10$
• Weight: $8$
• Character orbit: 10.b
• Rep. character: $\chi_{10}(9,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(10, [\chi])\).

	Total	New	Old
Modular forms	12	4	8
Cusp forms	8	4	4
Eisenstein series	4	0	4

Trace form

4 * q - 256 * q^4 + 60 * q^5 + 896 * q^6 - 6788 * q^9 - 640 * q^10 + 17808 * q^11 - 6528 * q^14 - 34960 * q^15 + 16384 * q^16 + 63600 * q^19 - 3840 * q^20 - 63952 * q^21 - 57344 * q^24 + 86100 * q^25 - 56064 * q^26 + 169560 * q^29 + 410240 * q^30 - 394112 * q^31 - 698368 * q^34 - 276720 * q^35 + 434432 * q^36 + 1163424 * q^39 + 40960 * q^40 + 232488 * q^41 - 1139712 * q^44 - 2879420 * q^45 + 1146496 * q^46 + 2520108 * q^49 + 2361600 * q^50 + 361088 * q^51 - 5116160 * q^54 - 526480 * q^55 + 417792 * q^56 + 2093520 * q^59 + 2237440 * q^60 - 5251432 * q^61 - 1048576 * q^64 + 2761440 * q^65 + 2401792 * q^66 + 6514864 * q^69 + 2679680 * q^70 - 7832352 * q^71 - 3126528 * q^74 - 7397600 * q^75 - 4070400 * q^76 + 7727040 * q^79 + 245760 * q^80 + 16428404 * q^81 + 4092928 * q^84 - 7995520 * q^85 + 4411776 * q^86 - 33470040 * q^89 - 15579520 * q^90 + 5340768 * q^91 + 15540352 * q^94 + 31904400 * q^95 + 3670016 * q^96 - 19109776 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(10, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
10.8.b.a	$10$	$8$	10.b	5.b	$2$	$4$	$4$	$3.124$	\(\Q(i, \sqrt{31})\)	None		✓	✓	✓	10.8.b.a	$2$	$0$	\(0\)	\(0\)	\(60\)	\(0\)	$2^{9}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(3\beta _{1}-\beta _{3})q^{3}-2^{6}q^{4}+(15+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(10, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)