Space of modular forms of level 633, weight 2, and trivial character

• Label: 633.2.a
• Level: $633$
• Weight: $2$
• Character orbit: 633.a
• Rep. character: $\chi_{633}(1,\cdot)$
• Character field: $\Q$
• Dimension: $35$
• Newform subspaces: $5$
• Sturm bound: $141$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 633 = 3 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	633.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(141\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(633))\).

	Total	New	Old
Modular forms	72	35	37
Cusp forms	69	35	34
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.

\(3\)	\(211\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(9\)
\(+\)	\(-\)	$-$	\(8\)
\(-\)	\(+\)	$-$	\(14\)
\(-\)	\(-\)	$+$	\(4\)
Plus space		\(+\)	\(13\)
Minus space		\(-\)	\(22\)

Trace form

\( 35 q + q^{2} + q^{3} + 39 q^{4} - 6 q^{5} + q^{6} + 9 q^{8} + 35 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(633))\) 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	211
633.2.a.a	$633$	$2$	633.a	1.a	$1$	$1$	$1$	$5.055$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-3\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}+2q^{7}+\cdots\)
633.2.a.b	$633$	$2$	633.a	1.a	$1$	$4$	$4$	$5.055$	4.4.725.1	None	✓	$1$	$1$	\(-2\)	\(4\)	\(-3\)	\(-11\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+q^{3}+(\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
633.2.a.c	$633$	$2$	633.a	1.a	$1$	$8$	$8$	$5.055$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(-8\)	\(-2\)	\(-11\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
633.2.a.d	$633$	$2$	633.a	1.a	$1$	$8$	$8$	$5.055$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(-8\)	\(3\)	\(7\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
633.2.a.e	$633$	$2$	633.a	1.a	$1$	$14$	$14$	$5.055$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(14\)	\(-1\)	\(13\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(633))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(633)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(211))\)\(^{\oplus 2}\)