Space of modular forms of level 2005, weight 2, and trivial character

• Label: 2005.2.a
• Level: $2005$
• Weight: $2$
• Character orbit: 2005.a
• Rep. character: $\chi_{2005}(1,\cdot)$
• Character field: $\Q$
• Dimension: $133$
• Newform subspaces: $7$
• Sturm bound: $402$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(402\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2005))\).

	Total	New	Old
Modular forms	202	133	69
Cusp forms	199	133	66
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.

\(5\)	\(401\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(29\)
\(+\)	\(-\)	$-$	\(37\)
\(-\)	\(+\)	$-$	\(37\)
\(-\)	\(-\)	$+$	\(30\)
Plus space		\(+\)	\(59\)
Minus space		\(-\)	\(74\)

Trace form

\( 133 q + 3 q^{2} + 131 q^{4} + q^{5} - 4 q^{6} - 4 q^{7} + 3 q^{8} + 141 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2005))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	401
2005.2.a.a	$2005$	$2$	2005.a	1.a	$1$	$1$	$1$	$16.010$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots\)
2005.2.a.b	$2005$	$2$	2005.a	1.a	$1$	$1$	$1$	$16.010$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots\)
2005.2.a.c	$2005$	$2$	2005.a	1.a	$1$	$3$	$3$	$16.010$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$1$	\(-3\)	\(-3\)	\(3\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
2005.2.a.d	$2005$	$2$	2005.a	1.a	$1$	$25$	$25$	$16.010$		None	✓	$1$	$1$	\(-5\)	\(-10\)	\(25\)	\(-31\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
2005.2.a.e	$2005$	$2$	2005.a	1.a	$1$	$29$	$29$	$16.010$		None	✓	$1$	$1$	\(-5\)	\(-3\)	\(-29\)	\(12\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
2005.2.a.f	$2005$	$2$	2005.a	1.a	$1$	$37$	$37$	$16.010$		None	✓	$1$	$0$	\(7\)	\(3\)	\(-37\)	\(-16\)		$+$	$-$	$-$		$\mathrm{SU}(2)$
2005.2.a.g	$2005$	$2$	2005.a	1.a	$1$	$37$	$37$	$16.010$		None	✓	$1$	$0$	\(11\)	\(13\)	\(37\)	\(34\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(401))\)\(^{\oplus 2}\)