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

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

Defining parameters

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	7.d (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{6})\)
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	10	10	0
Cusp forms	6	6	0
Eisenstein series	4	4	0

Trace form

6 * q + 4 * q^2 - 3 * q^3 - 20 * q^4 + 165 * q^5 - 406 * q^7 - 1312 * q^8 + 42 * q^9 + 2580 * q^10 + 403 * q^11 + 5964 * q^12 - 5936 * q^14 - 20910 * q^15 + 3064 * q^16 + 8229 * q^17 + 6672 * q^18 + 29985 * q^19 - 8967 * q^21 - 63584 * q^22 + 8383 * q^23 + 28872 * q^24 + 19950 * q^25 + 33768 * q^26 - 18004 * q^28 - 26588 * q^29 - 10560 * q^30 - 39399 * q^31 - 39072 * q^32 - 36711 * q^33 + 46305 * q^35 + 175488 * q^36 + 17707 * q^37 + 60960 * q^38 + 16548 * q^39 - 137280 * q^40 - 22344 * q^42 + 285388 * q^43 - 122652 * q^44 - 370530 * q^45 - 184592 * q^46 - 407823 * q^47 + 375438 * q^49 + 578800 * q^50 + 64809 * q^51 + 128856 * q^52 + 165043 * q^53 - 44496 * q^54 - 214480 * q^56 - 141534 * q^57 - 11696 * q^58 - 436299 * q^59 - 207900 * q^60 + 141201 * q^61 + 380898 * q^63 - 778720 * q^64 + 10500 * q^65 + 1025532 * q^66 + 701271 * q^67 + 799596 * q^68 - 1634640 * q^70 - 1277684 * q^71 + 141072 * q^72 - 421599 * q^73 - 688900 * q^74 + 826050 * q^75 + 1149967 * q^77 - 1268736 * q^78 + 573759 * q^79 + 2654040 * q^80 + 872505 * q^81 + 2585016 * q^82 - 1982148 * q^84 - 1677390 * q^85 - 947680 * q^86 - 1909746 * q^87 - 556648 * q^88 - 2990823 * q^89 + 711480 * q^91 + 1178376 * q^92 + 551337 * q^93 + 223584 * q^94 + 958485 * q^95 + 972720 * q^96 + 1050364 * q^98 + 1879428 * 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.d.a	$7$	$7$	7.d	7.d	$6$	$2$	$1$	$1.610$	\(\Q(\sqrt{-3}) \)	None		✓			7.7.d.a	$2$	$0$	\(12\)	\(-21\)	\(315\)	\(-686\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+12\zeta_{6}q^{2}+(-7-7\zeta_{6})q^{3}+(-80+\cdots)q^{4}+\cdots\)
7.7.d.b	$7$	$7$	7.d	7.d	$6$	$4$	$2$	$1.610$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓	✓		7.7.d.b	$2$	$0$	\(-8\)	\(18\)	\(-150\)	\(280\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-4-4\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(6+3\beta _{1}+\cdots)q^{3}+\cdots\)