Space of modular forms of level 7, weight 10, and Character 7.c

• Label: 7.10.c
• Level: $7$
• Weight: $10$
• Character orbit: 7.c
• Rep. character: $\chi_{7}(2,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(7, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	10	10	0
Eisenstein series	4	4	0

Trace form

10 * q - 18 * q^2 + 161 * q^3 - 940 * q^4 + 1533 * q^5 - 8708 * q^6 - 1036 * q^7 + 34272 * q^8 - 35734 * q^9 + 4298 * q^10 + 42213 * q^11 + 135604 * q^12 - 319676 * q^13 - 39522 * q^14 + 151394 * q^15 + 322064 * q^16 + 324681 * q^17 - 1012868 * q^18 - 16121 * q^19 - 350616 * q^20 - 1557857 * q^21 - 62692 * q^22 + 2638863 * q^23 + 8449728 * q^24 - 1304092 * q^25 + 4179252 * q^26 - 18331558 * q^27 - 22156316 * q^28 + 15292500 * q^29 + 20557942 * q^30 + 19179237 * q^31 - 6263520 * q^32 + 1689359 * q^33 - 62909700 * q^34 - 43746759 * q^35 + 71476528 * q^36 + 39566985 * q^37 + 67365270 * q^38 - 44299486 * q^39 + 5721744 * q^40 - 53436852 * q^41 - 183129856 * q^42 + 101835992 * q^43 + 99704916 * q^44 + 85098230 * q^45 - 14489202 * q^46 + 32509659 * q^47 - 185141600 * q^48 - 49024598 * q^49 + 3328464 * q^50 + 44168403 * q^51 + 103893272 * q^52 - 25714707 * q^53 + 51200926 * q^54 - 144695222 * q^55 + 115352832 * q^56 - 121710346 * q^57 - 46645516 * q^58 + 46776513 * q^59 + 132391756 * q^60 - 113075039 * q^61 + 467465628 * q^62 + 318071530 * q^63 - 192008960 * q^64 - 338113566 * q^65 - 836682602 * q^66 - 126707879 * q^67 + 32262636 * q^68 + 1323616182 * q^69 + 697712470 * q^70 - 1188736032 * q^71 - 950557728 * q^72 - 859257651 * q^73 + 591757530 * q^74 - 169061732 * q^75 + 1101475592 * q^76 + 1911891891 * q^77 + 519432424 * q^78 - 527065417 * q^79 - 1257352656 * q^80 + 551662715 * q^81 - 1341703076 * q^82 - 144863208 * q^83 + 486452204 * q^84 - 1197360222 * q^85 - 678648216 * q^86 - 340781350 * q^87 + 903700608 * q^88 + 1661554797 * q^89 + 1967758744 * q^90 + 726641384 * q^91 - 1301840952 * q^92 - 423057489 * q^93 - 272580882 * q^94 - 1197123495 * q^95 - 1441922272 * q^96 + 869770188 * q^97 - 2404833858 * q^98 - 1900777180 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(7, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7.10.c.a	$7$	$10$	7.c	7.c	$3$	$10$	$5$	$3.605$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓	✓	✓	7.10.c.a	$2$	$0$	\(-18\)	\(161\)	\(1533\)	\(-1036\)	$2^{12}\cdot 3^{3}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{2}-4\beta _{3})q^{2}+(33-\beta _{1}+\cdots)q^{3}+\cdots\)