Space of modular forms of level 890, weight 2, and trivial character

• Label: 890.2.a
• Level: $890$
• Weight: $2$
• Character orbit: 890.a
• Rep. character: $\chi_{890}(1,\cdot)$
• Character field: $\Q$
• Dimension: $31$
• Newform subspaces: $14$
• Sturm bound: $270$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 890 = 2 \cdot 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	890.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(270\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(890))\).

	Total	New	Old
Modular forms	138	31	107
Cusp forms	131	31	100
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.

\(2\)	\(5\)	\(89\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(4\)
\(+\)	\(+\)	\(-\)	$-$	\(4\)
\(+\)	\(-\)	\(+\)	$-$	\(6\)
\(+\)	\(-\)	\(-\)	$+$	\(2\)
\(-\)	\(+\)	\(+\)	$-$	\(5\)
\(-\)	\(+\)	\(-\)	$+$	\(3\)
\(-\)	\(-\)	\(+\)	$+$	\(1\)
\(-\)	\(-\)	\(-\)	$-$	\(6\)
Plus space			\(+\)	\(10\)
Minus space			\(-\)	\(21\)

Trace form

\( 31 q - q^{2} + 31 q^{4} - q^{5} - 4 q^{6} + 8 q^{7} - q^{8} + 35 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(890))\) 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	5	89
890.2.a.a	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
890.2.a.b	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}+2q^{7}+\cdots\)
890.2.a.c	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}-3q^{9}+\cdots\)
890.2.a.d	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
890.2.a.e	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(2\)	\(-1\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}+4q^{7}+\cdots\)
890.2.a.f	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-3\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{8}+\cdots\)
890.2.a.g	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
890.2.a.h	$890$	$2$	890.a	1.a	$1$	$1$	$1$	$7.107$	\(\Q\)	None	✓	$1$	$0$	\(1\)	\(0\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}-3q^{9}+\cdots\)
890.2.a.i	$890$	$2$	890.a	1.a	$1$	$2$	$2$	$7.107$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$1$	\(-2\)	\(-1\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}-2q^{7}+\cdots\)
890.2.a.j	$890$	$2$	890.a	1.a	$1$	$2$	$2$	$7.107$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(2\)	\(0\)	\(-2\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-q^{5}+(-3-\beta )q^{7}+q^{8}+\cdots\)
890.2.a.k	$890$	$2$	890.a	1.a	$1$	$3$	$3$	$7.107$	3.3.404.1	None	✓	$1$	$0$	\(-3\)	\(1\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
890.2.a.l	$890$	$2$	890.a	1.a	$1$	$5$	$5$	$7.107$	5.5.1186628.1	None	✓	$1$	$0$	\(5\)	\(1\)	\(-5\)	\(8\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{4}q^{3}+q^{4}-q^{5}+\beta _{4}q^{6}+\cdots\)
890.2.a.m	$890$	$2$	890.a	1.a	$1$	$5$	$5$	$7.107$	5.5.7736352.1	None	✓	$1$	$0$	\(5\)	\(1\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
890.2.a.n	$890$	$2$	890.a	1.a	$1$	$6$	$6$	$7.107$	6.6.387230992.1	None	✓	$1$	$0$	\(-6\)	\(3\)	\(6\)	\(6\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(890))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(890)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(178))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(445))\)\(^{\oplus 2}\)