Space of modular forms of level 894, weight 2, and trivial character

• Label: 894.2.a
• Level: $894$
• Weight: $2$
• Character orbit: 894.a
• Rep. character: $\chi_{894}(1,\cdot)$
• Character field: $\Q$
• Dimension: $25$
• Newform subspaces: $12$
• Sturm bound: $300$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 894 = 2 \cdot 3 \cdot 149 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	894.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(300\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(894))\).

	Total	New	Old
Modular forms	154	25	129
Cusp forms	147	25	122
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.

\(2\)	\(3\)	\(149\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(2\)
\(+\)	\(+\)	\(-\)	$-$	\(4\)
\(+\)	\(-\)	\(+\)	$-$	\(6\)
\(+\)	\(-\)	\(-\)	$+$	\(1\)
\(-\)	\(+\)	\(+\)	$-$	\(4\)
\(-\)	\(+\)	\(-\)	$+$	\(2\)
\(-\)	\(-\)	\(+\)	$+$	\(1\)
\(-\)	\(-\)	\(-\)	$-$	\(5\)
Plus space			\(+\)	\(6\)
Minus space			\(-\)	\(19\)

Trace form

\( 25 q - q^{2} + q^{3} + 25 q^{4} - 6 q^{5} - q^{6} - 4 q^{7} - q^{8} + 25 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(894))\) 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	149
894.2.a.a	$894$	$2$	894.a	1.a	$1$	$1$	$1$	$7.139$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(-3\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots\)
894.2.a.b	$894$	$2$	894.a	1.a	$1$	$1$	$1$	$7.139$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-1\)	\(0\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
894.2.a.c	$894$	$2$	894.a	1.a	$1$	$1$	$1$	$7.139$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
894.2.a.d	$894$	$2$	894.a	1.a	$1$	$1$	$1$	$7.139$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(1\)	\(3\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+2q^{7}+\cdots\)
894.2.a.e	$894$	$2$	894.a	1.a	$1$	$1$	$1$	$7.139$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(-3\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+2q^{7}+\cdots\)
894.2.a.f	$894$	$2$	894.a	1.a	$1$	$1$	$1$	$7.139$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(-1\)	\(0\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
894.2.a.g	$894$	$2$	894.a	1.a	$1$	$1$	$1$	$7.139$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(1\)	\(-3\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-4q^{7}+\cdots\)
894.2.a.h	$894$	$2$	894.a	1.a	$1$	$2$	$2$	$7.139$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(2\)	\(2\)	\(-1\)	\(8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}-\beta q^{5}+q^{6}+4q^{7}+\cdots\)
894.2.a.i	$894$	$2$	894.a	1.a	$1$	$3$	$3$	$7.139$	\(\Q(\zeta_{18})^+\)	None	✓	$1$	$0$	\(3\)	\(3\)	\(3\)	\(-3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)
894.2.a.j	$894$	$2$	894.a	1.a	$1$	$4$	$4$	$7.139$	4.4.6809.1	None	✓	$1$	$0$	\(-4\)	\(-4\)	\(2\)	\(-7\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+q^{6}+\cdots\)
894.2.a.k	$894$	$2$	894.a	1.a	$1$	$4$	$4$	$7.139$	4.4.15529.1	None	✓	$1$	$0$	\(4\)	\(-4\)	\(0\)	\(3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}+q^{4}+(\beta _{2}-\beta _{3})q^{5}-q^{6}+\cdots\)
894.2.a.l	$894$	$2$	894.a	1.a	$1$	$5$	$5$	$7.139$	5.5.5444689.1	None	✓	$1$	$0$	\(-5\)	\(5\)	\(-5\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{1}+\beta _{4})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(894))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(894)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(149))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(298))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(447))\)\(^{\oplus 2}\)