Space of modular forms of level 880, weight 2, and trivial character

• Label: 880.2.a
• Level: $880$
• Weight: $2$
• Character orbit: 880.a
• Rep. character: $\chi_{880}(1,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $15$
• Sturm bound: $288$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(288\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(880))\).

	Total	New	Old
Modular forms	156	20	136
Cusp forms	133	20	113
Eisenstein series	23	0	23

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

\(2\)	\(5\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(15\)	\(3\)	\(12\)		\(13\)	\(3\)	\(10\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)		\(24\)	\(3\)	\(21\)		\(21\)	\(3\)	\(18\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)		\(21\)	\(2\)	\(19\)		\(18\)	\(2\)	\(16\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)		\(18\)	\(2\)	\(16\)		\(15\)	\(2\)	\(13\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)		\(20\)	\(3\)	\(17\)		\(17\)	\(3\)	\(14\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)		\(19\)	\(1\)	\(18\)		\(16\)	\(1\)	\(15\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)		\(22\)	\(2\)	\(20\)		\(19\)	\(2\)	\(17\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)		\(17\)	\(4\)	\(13\)		\(14\)	\(4\)	\(10\)		\(3\)	\(0\)	\(3\)
Plus space			\(+\)		\(74\)	\(8\)	\(66\)		\(63\)	\(8\)	\(55\)		\(11\)	\(0\)	\(11\)
Minus space			\(-\)		\(82\)	\(12\)	\(70\)		\(70\)	\(12\)	\(58\)		\(12\)	\(0\)	\(12\)

Trace form

20 * q - 4 * q^3 - 8 * q^7 + 20 * q^9 + 4 * q^15 + 8 * q^21 + 12 * q^23 + 20 * q^25 + 8 * q^27 + 8 * q^29 - 24 * q^31 + 16 * q^39 - 32 * q^43 + 8 * q^45 + 20 * q^47 + 4 * q^49 + 48 * q^51 + 4 * q^55 - 16 * q^57 + 32 * q^59 - 16 * q^61 + 8 * q^63 - 20 * q^67 - 8 * q^69 - 16 * q^71 - 16 * q^73 - 4 * q^75 + 12 * q^81 + 16 * q^83 - 16 * q^85 + 24 * q^87 - 32 * q^91 - 48 * q^93 - 8 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(880))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5	11
880.2.a.a	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	\(\Q\)	None	✓				440.2.a.d	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{5}-q^{7}+6q^{9}+q^{11}-6q^{13}+\cdots\)
880.2.a.b	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	\(\Q\)	None	✓				220.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+q^{9}-q^{11}-2q^{15}+\cdots\)
880.2.a.c	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	\(\Q\)	None	✓				110.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-5q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots\)
880.2.a.d	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	\(\Q\)	None	✓		✓	✓	110.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots\)
880.2.a.e	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	\(\Q\)	None	✓				440.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{9}-q^{11}-4q^{13}+\cdots\)
880.2.a.f	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	\(\Q\)	None	✓				440.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{9}+q^{11}+8q^{19}+\cdots\)
880.2.a.g	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	\(\Q\)	None	✓				440.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-3q^{9}+q^{11}+6q^{13}+\cdots\)
880.2.a.h	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	\(\Q\)	None	✓				55.2.a.a	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}+q^{11}+2q^{13}+6q^{17}+\cdots\)
880.2.a.i	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	\(\Q\)	None	✓				110.2.a.b	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}-2q^{9}-q^{11}-6q^{13}+\cdots\)
880.2.a.j	$880$	$2$	880.a	1.a	$1$	$1$	$1$	$7.027$	\(\Q\)	None	✓				220.2.a.a	$1$	$0$	\(0\)	\(2\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+4q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
880.2.a.k	$880$	$2$	880.a	1.a	$1$	$2$	$2$	$7.027$	\(\Q(\sqrt{17}) \)	None	✓		✓		440.2.a.g	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(-5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+(-2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
880.2.a.l	$880$	$2$	880.a	1.a	$1$	$2$	$2$	$7.027$	\(\Q(\sqrt{17}) \)	None	✓		✓		440.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
880.2.a.m	$880$	$2$	880.a	1.a	$1$	$2$	$2$	$7.027$	\(\Q(\sqrt{2}) \)	None	✓		✓		55.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+2q^{7}+5q^{9}-q^{11}+\cdots\)
880.2.a.n	$880$	$2$	880.a	1.a	$1$	$2$	$2$	$7.027$	\(\Q(\sqrt{33}) \)	None	✓		✓		110.2.a.d	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}-\beta q^{7}+(5+\beta )q^{9}+q^{11}+\cdots\)
880.2.a.o	$880$	$2$	880.a	1.a	$1$	$2$	$2$	$7.027$	\(\Q(\sqrt{17}) \)	None	✓		✓	✓	440.2.a.e	$1$	$0$	\(0\)	\(1\)	\(2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}+\beta q^{7}+(1+\beta )q^{9}-q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(880))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(880)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 2}\)