Space of modular forms of level 1148, weight 2, and trivial character

• Label: 1148.2.a
• Level: $1148$
• Weight: $2$
• Character orbit: 1148.a
• Rep. character: $\chi_{1148}(1,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $5$
• Sturm bound: $336$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(336\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1148))\).

	Total	New	Old
Modular forms	174	20	154
Cusp forms	163	20	143
Eisenstein series	11	0	11

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

\(2\)	\(7\)	\(41\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(-\)	$+$	\(5\)
\(-\)	\(-\)	\(+\)	$+$	\(5\)
\(-\)	\(-\)	\(-\)	$-$	\(5\)
Plus space			\(+\)	\(10\)
Minus space			\(-\)	\(10\)

Trace form

\( 20 q - 4 q^{3} - 4 q^{5} + 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1148))\) 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	7	41
1148.2.a.a	$1148$	$2$	1148.a	1.a	$1$	$2$	$2$	$9.167$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+\cdots\)
1148.2.a.b	$1148$	$2$	1148.a	1.a	$1$	$3$	$3$	$9.167$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+(-2\beta _{1}+2\beta _{2})q^{5}+\cdots\)
1148.2.a.c	$1148$	$2$	1148.a	1.a	$1$	$5$	$5$	$9.167$	5.5.470117.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}-q^{7}+\cdots\)
1148.2.a.d	$1148$	$2$	1148.a	1.a	$1$	$5$	$5$	$9.167$	5.5.287349.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(-5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}-q^{7}+\cdots\)
1148.2.a.e	$1148$	$2$	1148.a	1.a	$1$	$5$	$5$	$9.167$	5.5.1935333.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(3\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1+\beta _{4})q^{5}+q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1148))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1148)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(164))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(574))\)\(^{\oplus 2}\)