Space of modular forms of level 2668, weight 2, and trivial character

• Label: 2668.2.a
• Level: $2668$
• Weight: $2$
• Character orbit: 2668.a
• Rep. character: $\chi_{2668}(1,\cdot)$
• Character field: $\Q$
• Dimension: $50$
• Newform subspaces: $5$
• Sturm bound: $720$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 2668 = 2^{2} \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2668.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(720\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2668))\).

	Total	New	Old
Modular forms	366	50	316
Cusp forms	355	50	305
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.

\(2\)	\(23\)	\(29\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	$-$	\(12\)
\(-\)	\(+\)	\(-\)	$+$	\(13\)
\(-\)	\(-\)	\(+\)	$+$	\(10\)
\(-\)	\(-\)	\(-\)	$-$	\(15\)
Plus space			\(+\)	\(23\)
Minus space			\(-\)	\(27\)

Trace form

\( 50 q + 4 q^{3} - 4 q^{7} + 50 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2668))\) 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	23	29
2668.2.a.a	$2668$	$2$	2668.a	1.a	$1$	$1$	$1$	$21.304$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+2q^{5}+q^{9}-2q^{13}-4q^{15}+\cdots\)
2668.2.a.b	$2668$	$2$	2668.a	1.a	$1$	$10$	$10$	$21.304$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{5}+\beta _{7}-\beta _{8})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots\)
2668.2.a.c	$2668$	$2$	2668.a	1.a	$1$	$12$	$12$	$21.304$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(5\)	\(0\)	\(3\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{8}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
2668.2.a.d	$2668$	$2$	2668.a	1.a	$1$	$13$	$13$	$21.304$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-7\)	\(0\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-\beta _{4}q^{5}-\beta _{7}q^{7}+(1+\cdots)q^{9}+\cdots\)
2668.2.a.e	$2668$	$2$	2668.a	1.a	$1$	$14$	$14$	$21.304$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(11\)	\(-2\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+\beta _{8}q^{5}-\beta _{5}q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2668))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2668)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(667))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1334))\)\(^{\oplus 2}\)