Space of modular forms of level 5, weight 9, and Character 5.c

• Label: 5.9.c
• Level: $5$
• Weight: $9$
• Character orbit: 5.c
• Rep. character: $\chi_{5}(2,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(4\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(5, [\chi])\).

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

Trace form

6 * q - 2 * q^2 - 72 * q^3 + 220 * q^5 + 1752 * q^6 - 2352 * q^7 - 8220 * q^8 + 30870 * q^10 + 23192 * q^11 - 45912 * q^12 - 119142 * q^13 + 241440 * q^15 + 218616 * q^16 - 265502 * q^17 - 454062 * q^18 + 412260 * q^20 + 231672 * q^21 - 35664 * q^22 + 28888 * q^23 - 340350 * q^25 - 801388 * q^26 + 392040 * q^27 + 1305192 * q^28 - 2549760 * q^30 - 747648 * q^31 + 3033928 * q^32 + 4269096 * q^33 - 4971680 * q^35 - 3972804 * q^36 - 454002 * q^37 + 1443720 * q^38 + 2683500 * q^40 + 2489432 * q^41 + 4223856 * q^42 + 792648 * q^43 + 210690 * q^45 - 3149928 * q^46 - 15313352 * q^47 - 21677712 * q^48 + 29537650 * q^50 + 35567712 * q^51 - 735732 * q^52 - 13509122 * q^53 + 4448040 * q^55 - 18454800 * q^56 - 34625520 * q^57 - 23903520 * q^58 + 13688520 * q^60 + 24111192 * q^61 + 53913416 * q^62 + 44837688 * q^63 - 30943610 * q^65 - 55047936 * q^66 - 32827752 * q^67 + 8118692 * q^68 - 44156280 * q^70 - 13992928 * q^71 + 82596420 * q^72 + 111859638 * q^73 - 126793200 * q^75 - 56470800 * q^76 + 26260136 * q^77 + 31125576 * q^78 + 23045920 * q^80 + 65834226 * q^81 + 38023056 * q^82 - 14768432 * q^83 - 19713030 * q^85 - 135560008 * q^86 - 133207680 * q^87 - 44555040 * q^88 + 135147990 * q^90 + 167542032 * q^91 + 69931048 * q^92 - 96798024 * q^93 + 239661000 * q^95 + 184867872 * q^96 - 186656202 * q^97 - 345959698 * q^98

Decomposition of \(S_{9}^{\mathrm{new}}(5, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5.9.c.a	$5$	$9$	5.c	5.c	$4$	$6$	$3$	$2.037$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		✓	✓	✓	5.9.c.a	$2$	$0$	\(-2\)	\(-72\)	\(220\)	\(-2352\)	$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}+(-12-12\beta _{1}-\beta _{2}-\beta _{5})q^{3}+\cdots\)