Space of modular forms of level 2007, weight 2, and trivial character

• Label: 2007.2.a
• Level: $2007$
• Weight: $2$
• Character orbit: 2007.a
• Rep. character: $\chi_{2007}(1,\cdot)$
• Character field: $\Q$
• Dimension: $93$
• Newform subspaces: $15$
• Sturm bound: $448$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2007 = 3^{2} \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2007.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(448\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2007))\).

	Total	New	Old
Modular forms	228	93	135
Cusp forms	221	93	128
Eisenstein series	7	0	7

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

\(3\)	\(223\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(12\)
\(+\)	\(-\)	$-$	\(26\)
\(-\)	\(+\)	$-$	\(31\)
\(-\)	\(-\)	$+$	\(24\)
Plus space		\(+\)	\(36\)
Minus space		\(-\)	\(57\)

Trace form

\( 93 q + 2 q^{2} + 92 q^{4} + 6 q^{5} + 4 q^{7} + 12 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2007))\) 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	223
2007.2.a.a	$2007$	$2$	2007.a	1.a	$1$	$1$	$1$	$16.026$	\(\Q\)	None	✓	$1$	$2$	\(-1\)	\(0\)	\(-3\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-3q^{5}-4q^{7}+3q^{8}+3q^{10}+\cdots\)
2007.2.a.b	$2007$	$2$	2007.a	1.a	$1$	$2$	$2$	$16.026$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(6\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{4}+3q^{5}-2\beta q^{7}+\cdots\)
2007.2.a.c	$2007$	$2$	2007.a	1.a	$1$	$2$	$2$	$16.026$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(-4+2\beta )q^{7}+\cdots\)
2007.2.a.d	$2007$	$2$	2007.a	1.a	$1$	$2$	$2$	$16.026$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(4\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(2-\beta )q^{5}+\cdots\)
2007.2.a.e	$2007$	$2$	2007.a	1.a	$1$	$2$	$2$	$16.026$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(6\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(3+\beta )q^{5}+\cdots\)
2007.2.a.f	$2007$	$2$	2007.a	1.a	$1$	$3$	$3$	$16.026$	3.3.148.1	None	✓	$1$	$1$	\(1\)	\(0\)	\(5\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2-\beta _{1})q^{5}+\cdots\)
2007.2.a.g	$2007$	$2$	2007.a	1.a	$1$	$3$	$3$	$16.026$	3.3.257.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-2\beta _{1}q^{5}-\beta _{1}q^{7}+\cdots\)
2007.2.a.h	$2007$	$2$	2007.a	1.a	$1$	$3$	$3$	$16.026$	3.3.321.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{7}+\cdots\)
2007.2.a.i	$2007$	$2$	2007.a	1.a	$1$	$4$	$4$	$16.026$	4.4.1957.1	None	✓	$1$	$0$	\(4\)	\(0\)	\(3\)	\(-6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
2007.2.a.j	$2007$	$2$	2007.a	1.a	$1$	$6$	$6$	$16.026$	6.6.3356224.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-12\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{4}+\beta _{5})q^{5}+\cdots\)
2007.2.a.k	$2007$	$2$	2007.a	1.a	$1$	$6$	$6$	$16.026$	6.6.74097664.1	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{1}q^{5}-\beta _{2}q^{7}+\cdots\)
2007.2.a.l	$2007$	$2$	2007.a	1.a	$1$	$7$	$7$	$16.026$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
2007.2.a.m	$2007$	$2$	2007.a	1.a	$1$	$12$	$12$	$16.026$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(-7\)	\(0\)	\(-7\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2007.2.a.n	$2007$	$2$	2007.a	1.a	$1$	$14$	$14$	$16.026$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(14\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{11}q^{5}+(1+\cdots)q^{7}+\cdots\)
2007.2.a.o	$2007$	$2$	2007.a	1.a	$1$	$26$	$26$	$16.026$		None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(20\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2007))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2007)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(223))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(669))\)\(^{\oplus 2}\)