Space of modular forms of level 10, weight 22, and Character 10.b

• Label: 10.22.b
• Level: $10$
• Weight: $22$
• Character orbit: 10.b
• Rep. character: $\chi_{10}(9,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $33$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
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:			\(33\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(10, [\chi])\).

	Total	New	Old
Modular forms	34	10	24
Cusp forms	30	10	20
Eisenstein series	4	0	4

Trace form

10 * q - 10485760 * q^4 + 27722150 * q^5 - 230748160 * q^6 - 12711922730 * q^9 - 22426931200 * q^10 - 199435236680 * q^11 - 104903905280 * q^14 - 1714785566200 * q^15 + 10995116277760 * q^16 + 123436918144200 * q^19 - 29068781158400 * q^20 - 158960071181080 * q^21 + 241956982620160 * q^24 - 753844388658750 * q^25 - 173073038991360 * q^26 + 1774546489874700 * q^29 + 5639638400921600 * q^30 + 10456190999441920 * q^31 - 18958190285946880 * q^34 + 24035281816377400 * q^35 + 13329417088532480 * q^36 + 45468500581785840 * q^39 + 23516341809971200 * q^40 + 93828363171915220 * q^41 + 209123002736967680 * q^44 - 1294878557826950 * q^45 - 453509186534543360 * q^46 - 1584589583512161570 * q^49 + 130953516753920000 * q^50 - 512256548145748480 * q^51 - 3219652987818598400 * q^54 + 8644481518774929800 * q^55 + 109999717382881280 * q^56 - 5722347962825378600 * q^59 + 1798082989863731200 * q^60 - 12650867843198554180 * q^61 - 11529215046068469760 * q^64 + 26346750548743534800 * q^65 - 32504410286103019520 * q^66 + 96951047157018456040 * q^69 + 41090423076705996800 * q^70 - 104781163131643184880 * q^71 + 32904860966761553920 * q^74 + 296606638041153670000 * q^75 - 129432989879972659200 * q^76 + 96531112322635730400 * q^79 + 30480826271950438400 * q^80 - 828031346148584406190 * q^81 + 166681715598772142080 * q^84 + 634500251198792806400 * q^85 - 1012021399291540418560 * q^86 + 1925821863958052788100 * q^89 + 598299873941928857600 * q^90 - 3491972396700191783280 * q^91 + 919679051426714398720 * q^94 + 1154253771449725323000 * q^95 - 253710285007916892160 * q^96 + 2120189706372537680840 * q^99

Decomposition of \(S_{22}^{\mathrm{new}}(10, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
10.22.b.a	$10$	$22$	10.b	5.b	$2$	$10$	$10$	$27.948$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓	✓	10.22.b.a	$2$	$0$	\(0\)	\(0\)	\(27722150\)	\(0\)	$2^{61}\cdot 3^{4}\cdot 5^{20}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(22\beta _{1}-\beta _{2})q^{3}-2^{20}q^{4}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{22}^{\mathrm{old}}(10, [\chi]) \simeq \) \(S_{22}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)