Space of modular forms of level 297, weight 2, and trivial character

• Label: 297.2.a
• Level: $297$
• Weight: $2$
• Character orbit: 297.a
• Rep. character: $\chi_{297}(1,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $8$
• Sturm bound: $72$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(72\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(297))\).

	Total	New	Old
Modular forms	42	14	28
Cusp forms	31	14	17
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.

\(3\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(3\)
\(+\)	\(-\)	$-$	\(5\)
\(-\)	\(+\)	$-$	\(4\)
\(-\)	\(-\)	$+$	\(2\)
Plus space		\(+\)	\(5\)
Minus space		\(-\)	\(9\)

Trace form

\( 14 q + 20 q^{4} - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(297))\) 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	11
297.2.a.a	$297$	$2$	297.a	1.a	$1$	$1$	$1$	$2.372$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-2q^{5}+q^{7}+4q^{10}+\cdots\)
297.2.a.b	$297$	$2$	297.a	1.a	$1$	$1$	$1$	$2.372$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(-5\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}-5q^{7}+3q^{8}-2q^{10}+\cdots\)
297.2.a.c	$297$	$2$	297.a	1.a	$1$	$1$	$1$	$2.372$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(-5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-2q^{5}-5q^{7}-3q^{8}-2q^{10}+\cdots\)
297.2.a.d	$297$	$2$	297.a	1.a	$1$	$1$	$1$	$2.372$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(2\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+2q^{5}+q^{7}+4q^{10}+\cdots\)
297.2.a.e	$297$	$2$	297.a	1.a	$1$	$2$	$2$	$2.372$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
297.2.a.f	$297$	$2$	297.a	1.a	$1$	$2$	$2$	$2.372$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(2\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
297.2.a.g	$297$	$2$	297.a	1.a	$1$	$3$	$3$	$2.372$	3.3.564.1	None	✓	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(7\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
297.2.a.h	$297$	$2$	297.a	1.a	$1$	$3$	$3$	$2.372$	3.3.564.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(7\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(297))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(297)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)