Space of modular forms of level 28, weight 6, and trivial character

• Label: 28.6.a
• Level: $28$
• Weight: $6$
• Character orbit: 28.a
• Rep. character: $\chi_{28}(1,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	28.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(28))\).

	Total	New	Old
Modular forms	23	2	21
Cusp forms	17	2	15
Eisenstein series	6	0	6

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

\(2\)	\(7\)	Fricke	Dim
\(-\)	\(+\)	\(-\)	\(1\)
\(-\)	\(-\)	\(+\)	\(1\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(1\)

Trace form

2 * q + 24 * q^3 - 80 * q^5 + 194 * q^9 - 712 * q^11 + 1256 * q^13 + 608 * q^15 - 964 * q^17 - 2792 * q^19 - 1372 * q^21 + 3440 * q^23 + 3222 * q^25 + 5904 * q^27 - 7628 * q^29 - 1456 * q^31 + 1648 * q^33 - 5488 * q^35 - 22268 * q^37 + 16640 * q^39 + 25356 * q^41 - 10088 * q^43 + 29872 * q^45 - 24624 * q^47 + 4802 * q^49 - 60176 * q^51 + 14124 * q^53 + 69248 * q^55 - 69960 * q^57 + 35944 * q^59 + 6560 * q^61 - 32928 * q^63 - 43968 * q^65 + 51240 * q^67 + 86752 * q^69 + 25088 * q^71 - 32364 * q^73 - 86776 * q^75 - 35672 * q^77 + 17648 * q^79 + 79370 * q^81 + 63704 * q^83 - 155872 * q^85 - 75856 * q^87 - 25404 * q^89 - 5488 * q^91 + 136976 * q^93 - 34144 * q^95 + 124284 * q^97 + 175544 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(28))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7
28.6.a.a	$28$	$6$	28.a	1.a	$1$	$1$	$1$	$4.491$	\(\Q\)	None	✓	✓	✓	✓	28.6.a.a	$1$	$1$	\(0\)	\(-2\)	\(-96\)	\(49\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-96q^{5}+7^{2}q^{7}-239q^{9}+\cdots\)
28.6.a.b	$28$	$6$	28.a	1.a	$1$	$1$	$1$	$4.491$	\(\Q\)	None	✓	✓	✓	✓	28.6.a.b	$1$	$0$	\(0\)	\(26\)	\(16\)	\(-49\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+26q^{3}+2^{4}q^{5}-7^{2}q^{7}+433q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(28))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(28)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)