Space of modular forms of level 4, weight 7, and Character 4.b

• Label: 4.7.b
• Level: $4$
• Weight: $7$
• Character orbit: 4.b
• Rep. character: $\chi_{4}(3,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $3$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(3\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(4, [\chi])\).

	Total	New	Old
Modular forms	4	4	0
Cusp forms	2	2	0
Eisenstein series	2	2	0

Trace form

2 * q + 4 * q^2 - 112 * q^4 + 20 * q^5 + 480 * q^6 - 704 * q^8 - 462 * q^9 + 40 * q^10 + 1920 * q^12 + 2932 * q^13 - 4800 * q^14 + 4352 * q^16 - 9532 * q^17 - 924 * q^18 - 1120 * q^20 + 19200 * q^21 + 14880 * q^22 - 23040 * q^24 - 31050 * q^25 + 5864 * q^26 - 19200 * q^28 + 50996 * q^29 + 4800 * q^30 + 62464 * q^32 - 59520 * q^33 - 19064 * q^34 + 25872 * q^36 + 3988 * q^37 - 116640 * q^38 - 7040 * q^40 + 58724 * q^41 + 38400 * q^42 + 59520 * q^44 - 4620 * q^45 + 162240 * q^46 - 215040 * q^48 + 43298 * q^49 - 62100 * q^50 - 164192 * q^52 - 385708 * q^53 + 239040 * q^54 + 230400 * q^56 + 466560 * q^57 + 101992 * q^58 + 19200 * q^60 - 21836 * q^61 - 648960 * q^62 - 28672 * q^64 + 29320 * q^65 - 119040 * q^66 + 533792 * q^68 - 648960 * q^69 - 48000 * q^70 + 162624 * q^72 + 577252 * q^73 + 7976 * q^74 - 466560 * q^76 + 595200 * q^77 + 703680 * q^78 + 43520 * q^80 - 1292958 * q^81 + 117448 * q^82 - 1075200 * q^84 - 95320 * q^85 + 333600 * q^86 - 714240 * q^88 + 621476 * q^89 - 9240 * q^90 + 648960 * q^92 + 2595840 * q^93 + 117120 * q^94 + 614400 * q^96 - 2914172 * q^97 + 86596 * q^98

Decomposition of \(S_{7}^{\mathrm{new}}(4, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4.7.b.a	$4$	$7$	4.b	4.b	$2$	$2$	$2$	$0.920$	\(\Q(\sqrt{-15}) \)	None		✓	✓	✓	4.7.b.a	$2$	$0$	\(4\)	\(0\)	\(20\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+\beta )q^{2}-4\beta q^{3}+(-56+4\beta )q^{4}+\cdots\)