Space of modular forms of level 7, weight 7, and Character 7.b

• Label: 7.7.b
• Level: $7$
• Weight: $7$
• Character orbit: 7.b
• Rep. character: $\chi_{7}(6,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $4$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	7.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(4\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	5	5	0
Cusp forms	3	3	0
Eisenstein series	2	2	0

Trace form

3 * q - 7 * q^2 + 17 * q^4 - 77 * q^7 + 601 * q^8 - 1893 * q^9 + 3710 * q^11 - 5215 * q^14 + 4080 * q^15 - 13087 * q^16 + 27537 * q^18 - 28560 * q^21 + 3674 * q^22 - 13258 * q^23 + 42795 * q^25 - 5831 * q^28 + 1070 * q^29 - 32640 * q^30 - 16983 * q^32 + 28560 * q^35 + 12393 * q^36 + 107198 * q^37 - 199920 * q^39 + 228480 * q^42 - 63778 * q^43 + 33354 * q^44 - 280414 * q^46 - 46893 * q^49 - 76735 * q^50 + 538560 * q^51 - 102466 * q^53 + 281281 * q^56 - 281520 * q^57 - 369334 * q^58 - 598773 * q^63 + 684721 * q^64 + 199920 * q^65 + 936558 * q^67 - 228480 * q^70 - 611290 * q^71 - 1650831 * q^72 + 862714 * q^74 - 440482 * q^77 + 1599360 * q^78 - 140490 * q^79 + 994563 * q^81 - 538560 * q^85 - 1642214 * q^86 + 65050 * q^88 - 1399440 * q^91 - 386478 * q^92 + 2480640 * q^93 + 281520 * q^95 + 2375177 * q^98 - 861330 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(7, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7.7.b.a	$7$	$7$	7.b	7.b	$2$	$1$	$1$	$1.610$	\(\Q\)	\(\Q(\sqrt{-7}) \)	✓	✓			7.7.b.a	$2$	$0$	\(9\)	\(0\)	\(0\)	\(-343\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+9q^{2}+17q^{4}-7^{3}q^{7}-423q^{8}+\cdots\)
7.7.b.b	$7$	$7$	7.b	7.b	$2$	$2$	$2$	$1.610$	\(\Q(\sqrt{-510}) \)	None		✓	✓		7.7.b.b	$2$	$0$	\(-16\)	\(0\)	\(0\)	\(266\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-8q^{2}+\beta q^{3}-\beta q^{5}-8\beta q^{6}+(133+\cdots)q^{7}+\cdots\)