Space of modular forms of level 2233, weight 2, and trivial character

• Label: 2233.2.a
• Level: $2233$
• Weight: $2$
• Character orbit: 2233.a
• Rep. character: $\chi_{2233}(1,\cdot)$
• Character field: $\Q$
• Dimension: $139$
• Newform subspaces: $13$
• Sturm bound: $480$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2233 = 7 \cdot 11 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2233.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(480\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2233))\).

	Total	New	Old
Modular forms	244	139	105
Cusp forms	237	139	98
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.

\(7\)	\(11\)	\(29\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(21\)
\(+\)	\(+\)	\(-\)	$-$	\(14\)
\(+\)	\(-\)	\(+\)	$-$	\(18\)
\(+\)	\(-\)	\(-\)	$+$	\(17\)
\(-\)	\(+\)	\(+\)	$-$	\(17\)
\(-\)	\(+\)	\(-\)	$+$	\(14\)
\(-\)	\(-\)	\(+\)	$+$	\(14\)
\(-\)	\(-\)	\(-\)	$-$	\(24\)
Plus space			\(+\)	\(66\)
Minus space			\(-\)	\(73\)

Trace form

\( 139 q - 3 q^{2} + 149 q^{4} - 2 q^{5} + 4 q^{6} - q^{7} - 15 q^{8} + 131 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2233))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	11	29
2233.2.a.a	$2233$	$2$	2233.a	1.a	$1$	$1$	$1$	$17.831$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots\)
2233.2.a.b	$2233$	$2$	2233.a	1.a	$1$	$1$	$1$	$17.831$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}+q^{7}-2q^{9}-q^{11}-2q^{12}+\cdots\)
2233.2.a.c	$2233$	$2$	2233.a	1.a	$1$	$2$	$2$	$17.831$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$0$	\(1\)	\(-2\)	\(-4\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+(1+\beta )q^{4}-2q^{5}-\beta q^{6}+\cdots\)
2233.2.a.d	$2233$	$2$	2233.a	1.a	$1$	$3$	$3$	$17.831$	3.3.148.1	None	✓	$1$	$0$	\(2\)	\(1\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
2233.2.a.e	$2233$	$2$	2233.a	1.a	$1$	$5$	$5$	$17.831$	5.5.2803624.1	None	✓	$1$	$1$	\(-1\)	\(-5\)	\(-2\)	\(5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
2233.2.a.f	$2233$	$2$	2233.a	1.a	$1$	$8$	$8$	$17.831$	8.8.4647835621.1	None	✓	$1$	$1$	\(-4\)	\(0\)	\(-3\)	\(8\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{5})q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)
2233.2.a.g	$2233$	$2$	2233.a	1.a	$1$	$13$	$13$	$17.831$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$0$	\(2\)	\(4\)	\(5\)	\(-13\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
2233.2.a.h	$2233$	$2$	2233.a	1.a	$1$	$14$	$14$	$17.831$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(-6\)	\(-7\)	\(-8\)	\(14\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
2233.2.a.i	$2233$	$2$	2233.a	1.a	$1$	$16$	$16$	$17.831$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$0$	\(-1\)	\(11\)	\(16\)	\(-16\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1-\beta _{8})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
2233.2.a.j	$2233$	$2$	2233.a	1.a	$1$	$17$	$17$	$17.831$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$1$	\(-2\)	\(-7\)	\(-10\)	\(-17\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{11}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
2233.2.a.k	$2233$	$2$	2233.a	1.a	$1$	$17$	$17$	$17.831$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$0$	\(7\)	\(4\)	\(1\)	\(17\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
2233.2.a.l	$2233$	$2$	2233.a	1.a	$1$	$21$	$21$	$17.831$		None	✓	$1$	$1$	\(-3\)	\(-4\)	\(-3\)	\(-21\)		$+$	$+$	$+$	$+$		$\mathrm{SU}(2)$
2233.2.a.m	$2233$	$2$	2233.a	1.a	$1$	$21$	$21$	$17.831$		None	✓	$1$	$0$	\(3\)	\(4\)	\(7\)	\(21\)		$-$	$-$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2233))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2233)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(203))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(319))\)\(^{\oplus 2}\)