Space of modular forms of level 21, weight 10, and Character 21.c

• Label: 21.10.c
• Level: $21$
• Weight: $10$
• Character orbit: 21.c
• Rep. character: $\chi_{21}(20,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $2$
• Sturm bound: $26$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	21.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(26\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(21, [\chi])\).

	Total	New	Old
Modular forms	26	26	0
Cusp forms	22	22	0
Eisenstein series	4	4	0

Trace form

22 * q - 5124 * q^4 + 5104 * q^7 + 32946 * q^9 - 198348 * q^15 + 1277060 * q^16 + 1669524 * q^18 - 1372314 * q^21 - 2268944 * q^22 + 2882362 * q^25 - 2158092 * q^28 - 12610356 * q^30 + 12847248 * q^36 - 18876724 * q^37 - 22458036 * q^39 + 30638076 * q^42 + 29758304 * q^43 + 129268936 * q^46 - 139260722 * q^49 - 204971400 * q^51 + 241573680 * q^57 + 773234056 * q^58 - 111000996 * q^60 + 288730212 * q^63 - 1013678084 * q^64 - 176203936 * q^67 - 327426120 * q^70 - 1841070444 * q^72 + 1985470404 * q^78 + 1881244016 * q^79 - 1257739794 * q^81 + 2676843828 * q^84 - 1567343952 * q^85 + 1671817664 * q^88 - 2920339728 * q^91 - 3400315284 * q^93 + 5421406848 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(21, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.10.c.a	$21$	$10$	21.c	21.c	$2$	$2$	$2$	$10.816$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			21.10.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(12580\)	$2\cdot 3^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q-3\beta q^{3}+512 q^{4}+(-19\beta+6290)q^{7}+\cdots\)
21.10.c.b	$21$	$10$	21.c	21.c	$2$	$20$	$20$	$10.816$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		21.10.c.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-7476\)	$2^{20}\cdot 3^{29}\cdot 7^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-307-\beta _{3})q^{4}+\cdots\)