Space of modular forms of level 21, weight 2, and trivial character

• Label: 21.2.a
• Level: $21$
• Weight: $2$
• Character orbit: 21.a
• Rep. character: $\chi_{21}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $5$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	21.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(5\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(21))\).

	Total	New	Old
Modular forms	4	1	3
Cusp forms	1	1	0
Eisenstein series	3	0	3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(7\)	Fricke	Dim
\(-\)	\(+\)	\(-\)	\(1\)
Plus space		\(+\)	\(0\)
Minus space		\(-\)	\(1\)

Trace form

q - q^2 + q^3 - q^4 - 2 * q^5 - q^6 - q^7 + 3 * q^8 + q^9 + 2 * q^10 + 4 * q^11 - q^12 - 2 * q^13 + q^14 - 2 * q^15 - q^16 - 6 * q^17 - q^18 + 4 * q^19 + 2 * q^20 - q^21 - 4 * q^22 + 3 * q^24 - q^25 + 2 * q^26 + q^27 + q^28 - 2 * q^29 + 2 * q^30 - 5 * q^32 + 4 * q^33 + 6 * q^34 + 2 * q^35 - q^36 + 6 * q^37 - 4 * q^38 - 2 * q^39 - 6 * q^40 + 2 * q^41 + q^42 - 4 * q^43 - 4 * q^44 - 2 * q^45 - q^48 + q^49 + q^50 - 6 * q^51 + 2 * q^52 + 6 * q^53 - q^54 - 8 * q^55 - 3 * q^56 + 4 * q^57 + 2 * q^58 + 12 * q^59 + 2 * q^60 - 2 * q^61 - q^63 + 7 * q^64 + 4 * q^65 - 4 * q^66 + 4 * q^67 + 6 * q^68 - 2 * q^70 + 3 * q^72 - 6 * q^73 - 6 * q^74 - q^75 - 4 * q^76 - 4 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 + q^81 - 2 * q^82 - 12 * q^83 + q^84 + 12 * q^85 + 4 * q^86 - 2 * q^87 + 12 * q^88 - 14 * q^89 + 2 * q^90 + 2 * q^91 - 8 * q^95 - 5 * q^96 + 18 * q^97 - q^98 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7
21.2.a.a	$21$	$2$	21.a	1.a	$1$	$1$	$1$	$0.168$	\(\Q\)	None	✓	✓	✓	✓	21.2.a.a	$1$	$0$	\(-1\)	\(1\)	\(-2\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)