Space of modular forms of level 453, weight 2, and trivial character

• Label: 453.2.a
• Level: $453$
• Weight: $2$
• Character orbit: 453.a
• Rep. character: $\chi_{453}(1,\cdot)$
• Character field: $\Q$
• Dimension: $25$
• Newform subspaces: $7$
• Sturm bound: $101$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 453 = 3 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	453.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(101\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(453))\).

	Total	New	Old
Modular forms	52	25	27
Cusp forms	49	25	24
Eisenstein series	3	0	3

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

\(3\)	\(151\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(8\)
\(+\)	\(-\)	$-$	\(4\)
\(-\)	\(+\)	$-$	\(11\)
\(-\)	\(-\)	$+$	\(2\)
Plus space		\(+\)	\(10\)
Minus space		\(-\)	\(15\)

Trace form

\( 25 q + q^{2} + q^{3} + 29 q^{4} - 6 q^{5} + 3 q^{6} + 4 q^{7} - 3 q^{8} + 25 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(453))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	151
453.2.a.a	$453$	$2$	453.a	1.a	$1$	$2$	$2$	$3.617$	\(\Q(\sqrt{5}) \)	None	✓	✓	453.2.a.a	$1$	$0$	\(-3\)	\(2\)	\(3\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(2-\beta )q^{5}+\cdots\)
453.2.a.b	$453$	$2$	453.a	1.a	$1$	$2$	$2$	$3.617$	\(\Q(\sqrt{5}) \)	None	✓	✓	453.2.a.b	$1$	$1$	\(-1\)	\(2\)	\(-1\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-1+\beta )q^{5}+\cdots\)
453.2.a.c	$453$	$2$	453.a	1.a	$1$	$2$	$2$	$3.617$	\(\Q(\sqrt{3}) \)	None	✓	✓	453.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{4}+2q^{5}-\beta q^{6}+q^{7}+\cdots\)
453.2.a.d	$453$	$2$	453.a	1.a	$1$	$2$	$2$	$3.617$	\(\Q(\sqrt{5}) \)	None	✓	✓	453.2.a.d	$1$	$0$	\(3\)	\(-2\)	\(-3\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(-2+\beta )q^{5}+\cdots\)
453.2.a.e	$453$	$2$	453.a	1.a	$1$	$3$	$3$	$3.617$	\(\Q(\zeta_{14})^+\)	None	✓	✓	453.2.a.e	$1$	$1$	\(-1\)	\(-3\)	\(-3\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
453.2.a.f	$453$	$2$	453.a	1.a	$1$	$5$	$5$	$3.617$	5.5.1190005.1	None	✓	✓	453.2.a.f	$1$	$1$	\(-3\)	\(-5\)	\(-4\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-q^{3}+(3-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
453.2.a.g	$453$	$2$	453.a	1.a	$1$	$9$	$9$	$3.617$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	453.2.a.g	$1$	$0$	\(6\)	\(9\)	\(-2\)	\(14\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+q^{3}+(1+\beta _{2}+\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(453))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(453)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(151))\)\(^{\oplus 2}\)