Space of modular forms of level 2268, weight 2, and trivial character

• Label: 2268.2.a
• Level: $2268$
• Weight: $2$
• Character orbit: 2268.a
• Rep. character: $\chi_{2268}(1,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $11$
• Sturm bound: $864$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(864\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2268))\).

	Total	New	Old
Modular forms	468	24	444
Cusp forms	397	24	373
Eisenstein series	71	0	71

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

\(2\)	\(3\)	\(7\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(-\)	$+$	\(5\)
\(-\)	\(-\)	\(+\)	$+$	\(7\)
\(-\)	\(-\)	\(-\)	$-$	\(7\)
Plus space			\(+\)	\(12\)
Minus space			\(-\)	\(12\)

Trace form

\( 24 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2268))\) 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	7
2268.2.a.a	$2268$	$2$	2268.a	1.a	$1$	$1$	$1$	$18.110$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-q^{7}-q^{11}+2q^{17}+2q^{19}+\cdots\)
2268.2.a.b	$2268$	$2$	2268.a	1.a	$1$	$1$	$1$	$18.110$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}-3q^{11}-4q^{13}+6q^{17}-4q^{19}+\cdots\)
2268.2.a.c	$2268$	$2$	2268.a	1.a	$1$	$1$	$1$	$18.110$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{7}+3q^{11}-4q^{13}-6q^{17}-4q^{19}+\cdots\)
2268.2.a.d	$2268$	$2$	2268.a	1.a	$1$	$1$	$1$	$18.110$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-q^{7}+q^{11}-2q^{17}+2q^{19}+\cdots\)
2268.2.a.e	$2268$	$2$	2268.a	1.a	$1$	$2$	$2$	$18.110$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2\beta q^{5}+q^{7}+\beta q^{11}-4q^{13}+2\beta q^{17}+\cdots\)
2268.2.a.f	$2268$	$2$	2268.a	1.a	$1$	$2$	$2$	$18.110$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+q^{7}+2\beta q^{11}+5q^{13}+\beta q^{17}+\cdots\)
2268.2.a.g	$2268$	$2$	2268.a	1.a	$1$	$3$	$3$	$18.110$	3.3.321.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(3\)		$-$	$+$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+q^{7}+(-2-\beta _{1})q^{11}+\cdots\)
2268.2.a.h	$2268$	$2$	2268.a	1.a	$1$	$3$	$3$	$18.110$	3.3.321.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}-q^{7}+(-1-\beta _{1}-2\beta _{2})q^{11}+\cdots\)
2268.2.a.i	$2268$	$2$	2268.a	1.a	$1$	$3$	$3$	$18.110$	3.3.321.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}-q^{7}+(1+\beta _{1}+2\beta _{2})q^{11}+\cdots\)
2268.2.a.j	$2268$	$2$	2268.a	1.a	$1$	$3$	$3$	$18.110$	3.3.321.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(3\)		$-$	$-$	$-$	$-$	$3$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{5}+q^{7}+(2+\beta _{1})q^{11}-q^{13}+\cdots\)
2268.2.a.k	$2268$	$2$	2268.a	1.a	$1$	$4$	$4$	$18.110$	\(\Q(\sqrt{3}, \sqrt{19})\)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}-q^{7}+(-\beta _{1}-\beta _{2})q^{11}+(-2+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2268))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2268)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(324))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(567))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(756))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1134))\)\(^{\oplus 2}\)