Space of modular forms of level 279, weight 2, and trivial character

• Label: 279.2.a
• Level: $279$
• Weight: $2$
• Character orbit: 279.a
• Rep. character: $\chi_{279}(1,\cdot)$
• Character field: $\Q$
• Dimension: $13$
• Newform subspaces: $4$
• Sturm bound: $64$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	279.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(64\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(279))\).

	Total	New	Old
Modular forms	36	13	23
Cusp forms	29	13	16
Eisenstein series	7	0	7

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

\(3\)	\(31\)	Fricke	Dim
\(+\)	\(-\)	$-$	\(6\)
\(-\)	\(+\)	$-$	\(5\)
\(-\)	\(-\)	$+$	\(2\)
Plus space		\(+\)	\(2\)
Minus space		\(-\)	\(11\)

Trace form

\( 13 q + 2 q^{2} + 16 q^{4} + 4 q^{5} + 4 q^{7} + 9 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(279))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	31
279.2.a.a	$279$	$2$	279.a	1.a	$1$	$2$	$2$	$2.228$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(-3+2\beta )q^{7}+\cdots\)
279.2.a.b	$279$	$2$	279.a	1.a	$1$	$2$	$2$	$2.228$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(3\)	\(0\)	\(4\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}+(3-2\beta )q^{5}+(-1+\cdots)q^{7}+\cdots\)
279.2.a.c	$279$	$2$	279.a	1.a	$1$	$3$	$3$	$2.228$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
279.2.a.d	$279$	$2$	279.a	1.a	$1$	$6$	$6$	$2.228$	6.6.361944768.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}-\beta _{2}q^{5}+(1+\beta _{5})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(279))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(279)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 2}\)