Space of modular forms of level 2672, weight 2, and trivial character

• Label: 2672.2.a
• Level: $2672$
• Weight: $2$
• Character orbit: 2672.a
• Rep. character: $\chi_{2672}(1,\cdot)$
• Character field: $\Q$
• Dimension: $83$
• Newform subspaces: $16$
• Sturm bound: $672$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2672 = 2^{4} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2672.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(672\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2672))\).

	Total	New	Old
Modular forms	342	83	259
Cusp forms	331	83	248
Eisenstein series	11	0	11

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

\(2\)	\(167\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(21\)
\(+\)	\(-\)	$-$	\(21\)
\(-\)	\(+\)	$-$	\(26\)
\(-\)	\(-\)	$+$	\(15\)
Plus space		\(+\)	\(36\)
Minus space		\(-\)	\(47\)

Trace form

\( 83 q + 2 q^{3} - 2 q^{5} + 2 q^{7} + 79 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2672))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	167
2672.2.a.a	$2672$	$2$	2672.a	1.a	$1$	$1$	$1$	$21.336$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-q^{7}-3q^{9}-2q^{13}-2q^{17}+\cdots\)
2672.2.a.b	$2672$	$2$	2672.a	1.a	$1$	$2$	$2$	$21.336$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(7\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(1-2\beta )q^{5}+(4-\beta )q^{7}+\cdots\)
2672.2.a.c	$2672$	$2$	2672.a	1.a	$1$	$2$	$2$	$21.336$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-6\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-3q^{5}+(-1-\beta )q^{7}+\beta q^{9}+\cdots\)
2672.2.a.d	$2672$	$2$	2672.a	1.a	$1$	$2$	$2$	$21.336$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{3}+(1+\beta )q^{5}+3q^{7}+5q^{9}+\cdots\)
2672.2.a.e	$2672$	$2$	2672.a	1.a	$1$	$2$	$2$	$21.336$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(1-2\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
2672.2.a.f	$2672$	$2$	2672.a	1.a	$1$	$2$	$2$	$21.336$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+(3-\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
2672.2.a.g	$2672$	$2$	2672.a	1.a	$1$	$2$	$2$	$21.336$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-4\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-3+2\beta )q^{5}+3q^{7}+\cdots\)
2672.2.a.h	$2672$	$2$	2672.a	1.a	$1$	$3$	$3$	$21.336$	3.3.733.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}-q^{7}+(2+\beta _{2})q^{9}+(-3+\cdots)q^{11}+\cdots\)
2672.2.a.i	$2672$	$2$	2672.a	1.a	$1$	$3$	$3$	$21.336$	3.3.469.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
2672.2.a.j	$2672$	$2$	2672.a	1.a	$1$	$5$	$5$	$21.336$	5.5.826865.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(10\)	\(-9\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{3}+2q^{5}+(-2+\beta _{3}+\cdots)q^{7}+\cdots\)
2672.2.a.k	$2672$	$2$	2672.a	1.a	$1$	$7$	$7$	$21.336$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(-2\)	\(12\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{3})q^{3}+(\beta _{1}-\beta _{2}+\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots\)
2672.2.a.l	$2672$	$2$	2672.a	1.a	$1$	$7$	$7$	$21.336$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(6\)	\(0\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
2672.2.a.m	$2672$	$2$	2672.a	1.a	$1$	$9$	$9$	$21.336$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-8\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{8})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
2672.2.a.n	$2672$	$2$	2672.a	1.a	$1$	$12$	$12$	$21.336$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-5\)	\(-2\)	\(-10\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{9}q^{5}+(-1-\beta _{11})q^{7}+\cdots\)
2672.2.a.o	$2672$	$2$	2672.a	1.a	$1$	$12$	$12$	$21.336$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(4\)	\(-11\)		$-$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{3}-\beta _{8}q^{5}+(-1+\beta _{2})q^{7}+(3+\cdots)q^{9}+\cdots\)
2672.2.a.p	$2672$	$2$	2672.a	1.a	$1$	$12$	$12$	$21.336$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(8\)	\(4\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{9})q^{5}-\beta _{11}q^{7}+(2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2672))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2672)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(334))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(668))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1336))\)\(^{\oplus 2}\)