Space of modular forms of level 2676, weight 2, and trivial character

• Label: 2676.2.a
• Level: $2676$
• Weight: $2$
• Character orbit: 2676.a
• Rep. character: $\chi_{2676}(1,\cdot)$
• Character field: $\Q$
• Dimension: $38$
• Newform subspaces: $6$
• Sturm bound: $896$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2676 = 2^{2} \cdot 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2676.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(896\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2676))\).

	Total	New	Old
Modular forms	454	38	416
Cusp forms	443	38	405
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.

\(2\)	\(3\)	\(223\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	$-$	\(11\)
\(-\)	\(+\)	\(-\)	$+$	\(8\)
\(-\)	\(-\)	\(+\)	$+$	\(8\)
\(-\)	\(-\)	\(-\)	$-$	\(11\)
Plus space			\(+\)	\(16\)
Minus space			\(-\)	\(22\)

Trace form

\( 38 q - 4 q^{7} + 38 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2676))\) 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	3	223
2676.2.a.a	$2676$	$2$	2676.a	1.a	$1$	$1$	$1$	$21.368$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}+q^{9}+6q^{11}-6q^{13}+\cdots\)
2676.2.a.b	$2676$	$2$	2676.a	1.a	$1$	$2$	$2$	$21.368$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-2\beta )q^{5}+(2-2\beta )q^{7}+q^{9}+\cdots\)
2676.2.a.c	$2676$	$2$	2676.a	1.a	$1$	$5$	$5$	$21.368$	5.5.1710888.1	None	✓	$1$	$1$	\(0\)	\(-5\)	\(-6\)	\(3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(1-\beta _{4})q^{7}+\cdots\)
2676.2.a.d	$2676$	$2$	2676.a	1.a	$1$	$8$	$8$	$21.368$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(8\)	\(-5\)	\(-13\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-\beta _{4}+\beta _{5})q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots\)
2676.2.a.e	$2676$	$2$	2676.a	1.a	$1$	$11$	$11$	$21.368$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-11\)	\(5\)	\(-5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}-\beta _{10}q^{7}+q^{9}-\beta _{7}q^{11}+\cdots\)
2676.2.a.f	$2676$	$2$	2676.a	1.a	$1$	$11$	$11$	$21.368$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(11\)	\(5\)	\(11\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(1+\beta _{9})q^{7}+q^{9}+\beta _{5}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2676))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2676)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(223))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(446))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(669))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(892))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1338))\)\(^{\oplus 2}\)