Space of modular forms of level 1077, weight 2, and trivial character

• Label: 1077.2.a
• Level: $1077$
• Weight: $2$
• Character orbit: 1077.a
• Rep. character: $\chi_{1077}(1,\cdot)$
• Character field: $\Q$
• Dimension: $59$
• Newform subspaces: $11$
• Sturm bound: $240$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1077 = 3 \cdot 359 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1077.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(240\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1077))\).

	Total	New	Old
Modular forms	122	59	63
Cusp forms	119	59	60
Eisenstein series	3	0	3

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

\(3\)	\(359\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(12\)
\(+\)	\(-\)	$-$	\(18\)
\(-\)	\(+\)	$-$	\(17\)
\(-\)	\(-\)	$+$	\(12\)
Plus space		\(+\)	\(24\)
Minus space		\(-\)	\(35\)

Trace form

\( 59 q + q^{2} - q^{3} + 57 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{8} + 59 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1077))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	359
1077.2.a.a	$1077$	$2$	1077.a	1.a	$1$	$1$	$1$	$8.600$	\(\Q\)	None	✓	✓	1077.2.a.a	$1$	$2$	\(-1\)	\(-1\)	\(-3\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}-3q^{5}+q^{6}-3q^{7}+\cdots\)
1077.2.a.b	$1077$	$2$	1077.a	1.a	$1$	$1$	$1$	$8.600$	\(\Q\)	None	✓	✓	1077.2.a.b	$1$	$1$	\(-1\)	\(1\)	\(-4\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-4q^{5}-q^{6}+q^{7}+\cdots\)
1077.2.a.c	$1077$	$2$	1077.a	1.a	$1$	$1$	$1$	$8.600$	\(\Q\)	None	✓	✓	1077.2.a.c	$1$	$0$	\(1\)	\(1\)	\(-2\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-2q^{7}+\cdots\)
1077.2.a.d	$1077$	$2$	1077.a	1.a	$1$	$2$	$2$	$8.600$	\(\Q(\sqrt{17}) \)	None	✓	✓	1077.2.a.d	$1$	$1$	\(-2\)	\(2\)	\(1\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+(1-\beta )q^{5}-q^{6}+\cdots\)
1077.2.a.e	$1077$	$2$	1077.a	1.a	$1$	$2$	$2$	$8.600$	\(\Q(\sqrt{5}) \)	None	✓	✓	1077.2.a.e	$1$	$1$	\(-1\)	\(-2\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
1077.2.a.f	$1077$	$2$	1077.a	1.a	$1$	$2$	$2$	$8.600$	\(\Q(\sqrt{5}) \)	None	✓	✓	1077.2.a.f	$1$	$0$	\(-1\)	\(-2\)	\(5\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(3-\beta )q^{5}+\cdots\)
1077.2.a.g	$1077$	$2$	1077.a	1.a	$1$	$3$	$3$	$8.600$	3.3.229.1	None	✓	✓	1077.2.a.g	$1$	$1$	\(0\)	\(3\)	\(-3\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1077.2.a.h	$1077$	$2$	1077.a	1.a	$1$	$6$	$6$	$8.600$	6.6.485125.1	None	✓	✓	1077.2.a.h	$1$	$1$	\(-4\)	\(6\)	\(-7\)	\(-7\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{4}+\beta _{5})q^{2}+q^{3}+(2+\cdots)q^{4}+\cdots\)
1077.2.a.i	$1077$	$2$	1077.a	1.a	$1$	$10$	$10$	$8.600$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	1077.2.a.i	$1$	$1$	\(0\)	\(-10\)	\(6\)	\(-11\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{7}+\cdots)q^{5}+\cdots\)
1077.2.a.j	$1077$	$2$	1077.a	1.a	$1$	$15$	$15$	$8.600$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	✓	1077.2.a.j	$1$	$0$	\(5\)	\(-15\)	\(-3\)	\(12\)		$+$	$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{12}q^{5}+\cdots\)
1077.2.a.k	$1077$	$2$	1077.a	1.a	$1$	$16$	$16$	$8.600$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	✓	1077.2.a.k	$1$	$0$	\(5\)	\(16\)	\(11\)	\(11\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1077))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1077)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(359))\)\(^{\oplus 2}\)