Space of modular forms of level 10, weight 6, and Character 10.b

• Label: 10.6.b
• Level: $10$
• Weight: $6$
• Character orbit: 10.b
• Rep. character: $\chi_{10}(9,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(10, [\chi])\).

	Total	New	Old
Modular forms	10	2	8
Cusp forms	6	2	4
Eisenstein series	4	0	4

Trace form

2 * q - 32 * q^4 + 110 * q^5 - 112 * q^6 + 94 * q^9 - 80 * q^10 - 296 * q^11 + 1264 * q^14 - 280 * q^15 + 512 * q^16 - 4440 * q^19 - 1760 * q^20 + 4424 * q^21 + 1792 * q^24 + 5850 * q^25 - 5472 * q^26 + 540 * q^29 - 6160 * q^30 - 4096 * q^31 + 16384 * q^34 + 3160 * q^35 - 1504 * q^36 - 19152 * q^39 + 1280 * q^40 - 4796 * q^41 + 4736 * q^44 + 5170 * q^45 + 9968 * q^46 - 16314 * q^49 - 8800 * q^50 + 57344 * q^51 - 32480 * q^54 - 16280 * q^55 - 20224 * q^56 + 79480 * q^59 + 4480 * q^60 - 84596 * q^61 - 8192 * q^64 - 13680 * q^65 + 16576 * q^66 + 34888 * q^69 + 69520 * q^70 - 8496 * q^71 - 34976 * q^74 - 30800 * q^75 + 71040 * q^76 - 70560 * q^79 + 28160 * q^80 - 90838 * q^81 - 70784 * q^84 + 40960 * q^85 - 18352 * q^86 + 170420 * q^89 - 3760 * q^90 + 216144 * q^91 - 85456 * q^94 - 244200 * q^95 - 28672 * q^96 - 13912 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(10, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
10.6.b.a	$10$	$6$	10.b	5.b	$2$	$2$	$2$	$1.604$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	10.6.b.a	$2$	$0$	\(0\)	\(0\)	\(110\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{2}+7\beta q^{3}-16 q^{4}+(5\beta+55)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(10, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)