Space of modular forms of level 100, weight 2, and trivial character

• Label: 100.2.a
• Level: $100$
• Weight: $2$
• Character orbit: 100.a
• Rep. character: $\chi_{100}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	100.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(30\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(100))\).

	Total	New	Old
Modular forms	24	1	23
Cusp forms	7	1	6
Eisenstein series	17	0	17

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

\(2\)	\(5\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(6\)	\(0\)	\(6\)		\(1\)	\(0\)	\(1\)		\(5\)	\(0\)	\(5\)
\(+\)	\(-\)	\(-\)		\(7\)	\(0\)	\(7\)		\(1\)	\(0\)	\(1\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)		\(6\)	\(1\)	\(5\)		\(3\)	\(1\)	\(2\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)		\(5\)	\(0\)	\(5\)		\(2\)	\(0\)	\(2\)		\(3\)	\(0\)	\(3\)
Plus space		\(+\)		\(11\)	\(0\)	\(11\)		\(3\)	\(0\)	\(3\)		\(8\)	\(0\)	\(8\)
Minus space		\(-\)		\(13\)	\(1\)	\(12\)		\(4\)	\(1\)	\(3\)		\(9\)	\(0\)	\(9\)

Trace form

q + 2 * q^3 - 2 * q^7 + q^9 - 2 * q^13 + 6 * q^17 - 4 * q^19 - 4 * q^21 - 6 * q^23 - 4 * q^27 + 6 * q^29 - 4 * q^31 - 2 * q^37 - 4 * q^39 + 6 * q^41 + 10 * q^43 + 6 * q^47 - 3 * q^49 + 12 * q^51 + 6 * q^53 - 8 * q^57 + 12 * q^59 + 2 * q^61 - 2 * q^63 - 2 * q^67 - 12 * q^69 - 12 * q^71 - 2 * q^73 + 8 * q^79 - 11 * q^81 - 6 * q^83 + 12 * q^87 - 6 * q^89 + 4 * q^91 - 8 * q^93 - 2 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(100))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5
100.2.a.a	$100$	$2$	100.a	1.a	$1$	$1$	$1$	$0.799$	\(\Q\)	None	✓		✓	✓	20.2.a.a	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-2q^{7}+q^{9}-2q^{13}+6q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(100)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)