Space of modular forms of level 248, weight 2, and trivial character

• Label: 248.2.a
• Level: $248$
• Weight: $2$
• Character orbit: 248.a
• Rep. character: $\chi_{248}(1,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $5$
• Sturm bound: $64$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 248 = 2^{3} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	248.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(64\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(248))\).

	Total	New	Old
Modular forms	36	8	28
Cusp forms	29	8	21
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.

\(2\)	\(31\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(-\)	$-$	\(3\)
\(-\)	\(+\)	$-$	\(3\)
\(-\)	\(-\)	$+$	\(1\)
Plus space		\(+\)	\(2\)
Minus space		\(-\)	\(6\)

Trace form

\( 8 q + 2 q^{3} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(248))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	31
248.2.a.a	$248$	$2$	248.a	1.a	$1$	$1$	$1$	$1.980$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}-3q^{7}+q^{9}-2q^{11}+\cdots\)
248.2.a.b	$248$	$2$	248.a	1.a	$1$	$1$	$1$	$1.980$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
248.2.a.c	$248$	$2$	248.a	1.a	$1$	$1$	$1$	$1.980$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{5}-3q^{7}-3q^{9}+2q^{11}-4q^{13}+\cdots\)
248.2.a.d	$248$	$2$	248.a	1.a	$1$	$2$	$2$	$1.980$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(4\)	\(3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+(2-\beta )q^{5}+\beta q^{7}+q^{9}-2q^{11}+\cdots\)
248.2.a.e	$248$	$2$	248.a	1.a	$1$	$3$	$3$	$1.980$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(5\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{2})q^{3}+(-1+\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(248))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(248)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(124))\)\(^{\oplus 2}\)