Space of modular forms of level 10, weight 12, and Character 10.b

• Label: 10.12.b
• Level: $10$
• Weight: $12$
• Character orbit: 10.b
• Rep. character: $\chi_{10}(9,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
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:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(10, [\chi])\).

	Total	New	Old
Modular forms	18	6	12
Cusp forms	14	6	8
Eisenstein series	4	0	4

Trace form

6 * q - 6144 * q^4 + 530 * q^5 + 17024 * q^6 - 496022 * q^9 - 385920 * q^10 - 642728 * q^11 - 2125952 * q^14 - 698680 * q^15 + 6291456 * q^16 - 24109080 * q^19 - 542720 * q^20 + 125471192 * q^21 - 17432576 * q^24 - 181718850 * q^25 + 89251584 * q^26 - 256409820 * q^29 - 221514880 * q^30 + 458481792 * q^31 - 225288192 * q^34 - 697136360 * q^35 + 507926528 * q^36 + 1318797936 * q^39 + 395182080 * q^40 - 164768948 * q^41 + 658153472 * q^44 + 3174067390 * q^45 - 2956208256 * q^46 - 675514158 * q^49 + 3912262400 * q^50 - 13060087168 * q^51 - 6079189760 * q^54 + 3688644360 * q^55 + 2176974848 * q^56 + 17663962360 * q^59 + 715448320 * q^60 - 5020792428 * q^61 - 6442450944 * q^64 - 19996916880 * q^65 + 14496229888 * q^66 + 23117013976 * q^69 + 24956826240 * q^70 + 56788418832 * q^71 - 64135292672 * q^74 - 95499160400 * q^75 + 24687697920 * q^76 + 2602550880 * q^79 + 555745280 * q^80 - 7039907074 * q^81 - 128482500608 * q^84 - 85024210560 * q^85 + 111995790464 * q^86 + 249448412540 * q^89 + 225507463040 * q^90 - 184446766128 * q^91 - 337749482112 * q^94 + 104896380600 * q^95 + 17850957824 * q^96 + 520781125736 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(10, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
10.12.b.a	$10$	$12$	10.b	5.b	$2$	$6$	$6$	$7.683$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		✓	✓	✓	10.12.b.a	$2$	$0$	\(0\)	\(0\)	\(530\)	\(0\)	$2^{19}\cdot 5^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{1}+3\beta _{2})q^{3}-2^{10}q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(10, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)