Space of modular forms of level 4, weight 21, and Character 4.b

• Label: 4.21.b
• Level: $4$
• Weight: $21$
• Character orbit: 4.b
• Rep. character: $\chi_{4}(3,\cdot)$
• Character field: $\Q$
• Dimension: $9$
• Newform subspaces: $2$
• Sturm bound: $10$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(10\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(4, [\chi])\).

	Total	New	Old
Modular forms	11	11	0
Cusp forms	9	9	0
Eisenstein series	2	2	0

Trace form

\( 9 q - 628 q^{2} - 267504 q^{4} - 738494 q^{5} + 99460608 q^{6} + 1103532992 q^{8} - 6924577767 q^{9} + O(q^{10}) \)

Decomposition of \(S_{21}^{\mathrm{new}}(4, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4.21.b.a	$4$	$21$	4.b	4.b	$2$	$1$	$1$	$10.141$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-1024\)	\(0\)	\(-19306574\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{10}q^{2}+2^{20}q^{4}-19306574q^{5}+\cdots\)
4.21.b.b	$4$	$21$	4.b	4.b	$2$	$8$	$8$	$10.141$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(396\)	\(0\)	\(18568080\)	\(0\)	$2^{56}\cdot 3^{5}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(7^{2}+\beta _{1})q^{2}+(6-12\beta _{1}-\beta _{2})q^{3}+\cdots\)