Space of modular forms of level 880, weight 6, and trivial character

• Label: 880.6.a
• Level: $880$
• Weight: $6$
• Character orbit: 880.a
• Rep. character: $\chi_{880}(1,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $26$
• Sturm bound: $864$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	880.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 26 \)
Sturm bound:			\(864\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(880))\).

	Total	New	Old
Modular forms	732	100	632
Cusp forms	708	100	608
Eisenstein series	24	0	24

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
\(+\)	\(+\)	\(+\)	\(+\)		\(87\)	\(13\)	\(74\)		\(84\)	\(13\)	\(71\)		\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)		\(96\)	\(13\)	\(83\)		\(93\)	\(13\)	\(80\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)		\(93\)	\(12\)	\(81\)		\(90\)	\(12\)	\(78\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)		\(90\)	\(12\)	\(78\)		\(87\)	\(12\)	\(75\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)		\(92\)	\(13\)	\(79\)		\(89\)	\(13\)	\(76\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)		\(91\)	\(11\)	\(80\)		\(88\)	\(11\)	\(77\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)		\(94\)	\(12\)	\(82\)		\(91\)	\(12\)	\(79\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)		\(89\)	\(14\)	\(75\)		\(86\)	\(14\)	\(72\)		\(3\)	\(0\)	\(3\)
Plus space			\(+\)		\(362\)	\(48\)	\(314\)		\(350\)	\(48\)	\(302\)		\(12\)	\(0\)	\(12\)
Minus space			\(-\)		\(370\)	\(52\)	\(318\)		\(358\)	\(52\)	\(306\)		\(12\)	\(0\)	\(12\)

Trace form

100 * q - 36 * q^3 + 248 * q^7 + 8100 * q^9 + 900 * q^15 - 8832 * q^19 + 1640 * q^21 + 6348 * q^23 + 62500 * q^25 - 19128 * q^27 - 7960 * q^29 + 1512 * q^31 - 88176 * q^39 + 73952 * q^43 - 11800 * q^45 + 44180 * q^47 + 210836 * q^49 + 26800 * q^51 + 12100 * q^55 + 25776 * q^57 - 23264 * q^59 - 48080 * q^61 - 80888 * q^63 - 202420 * q^67 + 43160 * q^69 - 81296 * q^71 + 105136 * q^73 - 22500 * q^75 + 67200 * q^79 + 611260 * q^81 - 210416 * q^83 + 132400 * q^85 + 150936 * q^87 + 58112 * q^89 - 167328 * q^91 - 362352 * q^93 + 149208 * q^97

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(880))\) 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
880.6.a.a	$880$	$6$	880.a	1.a	$1$	$1$	$1$	$141.138$	\(\Q\)	None	✓				440.6.a.a	$1$	$2$	\(0\)	\(-23\)	\(25\)	\(-211\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-23q^{3}+5^{2}q^{5}-211q^{7}+286q^{9}+\cdots\)
880.6.a.b	$880$	$6$	880.a	1.a	$1$	$1$	$1$	$141.138$	\(\Q\)	None	✓				110.6.a.b	$1$	$1$	\(0\)	\(-12\)	\(-25\)	\(-54\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-12q^{3}-5^{2}q^{5}-54q^{7}-99q^{9}+\cdots\)
880.6.a.c	$880$	$6$	880.a	1.a	$1$	$1$	$1$	$141.138$	\(\Q\)	None	✓				110.6.a.a	$1$	$1$	\(0\)	\(-2\)	\(25\)	\(40\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+5^{2}q^{5}+40q^{7}-239q^{9}+\cdots\)
880.6.a.d	$880$	$6$	880.a	1.a	$1$	$1$	$1$	$141.138$	\(\Q\)	None	✓				110.6.a.d	$1$	$0$	\(0\)	\(2\)	\(25\)	\(204\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+5^{2}q^{5}+204q^{7}-239q^{9}+\cdots\)
880.6.a.e	$880$	$6$	880.a	1.a	$1$	$1$	$1$	$141.138$	\(\Q\)	None	✓				110.6.a.c	$1$	$0$	\(0\)	\(12\)	\(-25\)	\(-110\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+12q^{3}-5^{2}q^{5}-110q^{7}-99q^{9}+\cdots\)
880.6.a.f	$880$	$6$	880.a	1.a	$1$	$2$	$2$	$141.138$	\(\Q(\sqrt{889}) \)	None	✓				110.6.a.e	$1$	$0$	\(0\)	\(-21\)	\(-50\)	\(-35\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-10-\beta )q^{3}-5^{2}q^{5}+(-20+5\beta )q^{7}+\cdots\)
880.6.a.g	$880$	$6$	880.a	1.a	$1$	$2$	$2$	$141.138$	\(\Q(\sqrt{1321}) \)	None	✓				110.6.a.f	$1$	$1$	\(0\)	\(3\)	\(-50\)	\(-237\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-5^{2}q^{5}+(-11^{2}+5\beta )q^{7}+\cdots\)
880.6.a.h	$880$	$6$	880.a	1.a	$1$	$2$	$2$	$141.138$	\(\Q(\sqrt{1761}) \)	None	✓				220.6.a.a	$1$	$0$	\(0\)	\(19\)	\(50\)	\(131\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(10-\beta )q^{3}+5^{2}q^{5}+(68-5\beta )q^{7}+\cdots\)
880.6.a.i	$880$	$6$	880.a	1.a	$1$	$3$	$3$	$141.138$	3.3.709185.1	None	✓				110.6.a.h	$1$	$1$	\(0\)	\(-25\)	\(75\)	\(-159\)		$-$	$-$	$+$	$+$	$2\cdot 5$	$\mathrm{SU}(2)$	\(q+(-8-\beta _{2})q^{3}+5^{2}q^{5}+(-53-\beta _{1}+\cdots)q^{7}+\cdots\)
880.6.a.j	$880$	$6$	880.a	1.a	$1$	$3$	$3$	$141.138$	3.3.399324.1	None	✓				220.6.a.b	$1$	$0$	\(0\)	\(-1\)	\(75\)	\(155\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+5^{2}q^{5}+(50-7\beta _{1}+2\beta _{2})q^{7}+\cdots\)
880.6.a.k	$880$	$6$	880.a	1.a	$1$	$3$	$3$	$141.138$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓				110.6.a.g	$1$	$0$	\(0\)	\(7\)	\(75\)	\(-273\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(2+\beta _{1})q^{3}+5^{2}q^{5}+(-93+5\beta _{1}+\cdots)q^{7}+\cdots\)
880.6.a.l	$880$	$6$	880.a	1.a	$1$	$3$	$3$	$141.138$	3.3.21865.1	None	✓				55.6.a.a	$1$	$1$	\(0\)	\(36\)	\(75\)	\(102\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(11+3\beta _{1})q^{3}+5^{2}q^{5}+(2^{5}+\beta _{1}+\cdots)q^{7}+\cdots\)
880.6.a.m	$880$	$6$	880.a	1.a	$1$	$4$	$4$	$141.138$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				220.6.a.d	$1$	$0$	\(0\)	\(0\)	\(-100\)	\(30\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-5^{2}q^{5}+(8-2\beta _{1}+\beta _{2}+\beta _{3})q^{7}+\cdots\)
880.6.a.n	$880$	$6$	880.a	1.a	$1$	$4$	$4$	$141.138$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				55.6.a.b	$1$	$1$	\(0\)	\(0\)	\(-100\)	\(90\)		$-$	$+$	$-$	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}-5^{2}q^{5}+(17-6\beta _{1}-5\beta _{2}+\cdots)q^{7}+\cdots\)
880.6.a.o	$880$	$6$	880.a	1.a	$1$	$4$	$4$	$141.138$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				220.6.a.c	$1$	$1$	\(0\)	\(0\)	\(-100\)	\(250\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-5^{2}q^{5}+(63+\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
880.6.a.p	$880$	$6$	880.a	1.a	$1$	$5$	$5$	$141.138$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		220.6.a.e	$1$	$1$	\(0\)	\(-18\)	\(125\)	\(-130\)		$-$	$-$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(-4+\beta _{1})q^{3}+5^{2}q^{5}+(-26+\beta _{1}+\cdots)q^{7}+\cdots\)
880.6.a.q	$880$	$6$	880.a	1.a	$1$	$5$	$5$	$141.138$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				440.6.a.c	$1$	$1$	\(0\)	\(-2\)	\(125\)	\(-134\)		$+$	$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+5^{2}q^{5}+(-28+3\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
880.6.a.r	$880$	$6$	880.a	1.a	$1$	$5$	$5$	$141.138$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		55.6.a.c	$1$	$0$	\(0\)	\(0\)	\(125\)	\(-70\)		$-$	$-$	$-$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+5^{2}q^{5}+(-14+\beta _{1}+\beta _{4})q^{7}+\cdots\)
880.6.a.s	$880$	$6$	880.a	1.a	$1$	$5$	$5$	$141.138$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				440.6.a.b	$1$	$0$	\(0\)	\(2\)	\(125\)	\(250\)		$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+5^{2}q^{5}+(51-2\beta _{1}+\beta _{4})q^{7}+\cdots\)
880.6.a.t	$880$	$6$	880.a	1.a	$1$	$6$	$6$	$141.138$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				440.6.a.f	$1$	$1$	\(0\)	\(-12\)	\(-150\)	\(338\)		$+$	$+$	$+$	$+$	$2^{8}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{3}-5^{2}q^{5}+(56+\beta _{1}+\cdots)q^{7}+\cdots\)
880.6.a.u	$880$	$6$	880.a	1.a	$1$	$6$	$6$	$141.138$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓		✓		55.6.a.d	$1$	$0$	\(0\)	\(0\)	\(-150\)	\(66\)		$-$	$+$	$+$	$-$	$2^{9}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-5^{2}q^{5}+(11-\beta _{1}+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
880.6.a.v	$880$	$6$	880.a	1.a	$1$	$6$	$6$	$141.138$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				440.6.a.e	$1$	$0$	\(0\)	\(12\)	\(-150\)	\(62\)		$+$	$+$	$-$	$-$	$2^{8}$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{3}-5^{2}q^{5}+(10-\beta _{5})q^{7}+\cdots\)
880.6.a.w	$880$	$6$	880.a	1.a	$1$	$6$	$6$	$141.138$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓		✓		440.6.a.d	$1$	$0$	\(0\)	\(30\)	\(150\)	\(170\)		$+$	$-$	$+$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q+(5-\beta _{1})q^{3}+5^{2}q^{5}+(28+2\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
880.6.a.x	$880$	$6$	880.a	1.a	$1$	$7$	$7$	$141.138$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		440.6.a.i	$1$	$1$	\(0\)	\(-25\)	\(175\)	\(49\)		$+$	$-$	$-$	$+$	$2^{10}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-4+\beta _{1})q^{3}+5^{2}q^{5}+(7-\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
880.6.a.y	$880$	$6$	880.a	1.a	$1$	$7$	$7$	$141.138$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		440.6.a.h	$1$	$0$	\(0\)	\(-21\)	\(-175\)	\(-49\)		$+$	$+$	$-$	$-$	$2^{11}\cdot 11$	$\mathrm{SU}(2)$	\(q+(-3+\beta _{1})q^{3}-5^{2}q^{5}+(-7+\beta _{1}+\cdots)q^{7}+\cdots\)
880.6.a.z	$880$	$6$	880.a	1.a	$1$	$7$	$7$	$141.138$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		440.6.a.g	$1$	$1$	\(0\)	\(3\)	\(-175\)	\(-227\)		$+$	$+$	$+$	$+$	$2^{11}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-5^{2}q^{5}+(-2^{5}+\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(880))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(880)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 2}\)