Space of modular forms of level 1104, weight 6, and trivial character

• Label: 1104.6.a
• Level: $1104$
• Weight: $6$
• Character orbit: 1104.a
• Rep. character: $\chi_{1104}(1,\cdot)$
• Character field: $\Q$
• Dimension: $110$
• Newform subspaces: $27$
• Sturm bound: $1152$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1104 = 2^{4} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1104.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 27 \)
Sturm bound:			\(1152\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(1104))\).

	Total	New	Old
Modular forms	972	110	862
Cusp forms	948	110	838
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.

\(2\)	\(3\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(13\)
\(+\)	\(+\)	\(-\)	$-$	\(15\)
\(+\)	\(-\)	\(+\)	$-$	\(14\)
\(+\)	\(-\)	\(-\)	$+$	\(12\)
\(-\)	\(+\)	\(+\)	$-$	\(15\)
\(-\)	\(+\)	\(-\)	$+$	\(13\)
\(-\)	\(-\)	\(+\)	$+$	\(13\)
\(-\)	\(-\)	\(-\)	$-$	\(15\)
Plus space			\(+\)	\(51\)
Minus space			\(-\)	\(59\)

Trace form

\( 110 q - 18 q^{3} - 76 q^{5} + 124 q^{7} + 8910 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(1104))\) 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	23
1104.6.a.a	$1104$	$6$	1104.a	1.a	$1$	$1$	$1$	$177.064$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-9\)	\(-46\)	\(136\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}-46q^{5}+136q^{7}+3^{4}q^{9}+\cdots\)
1104.6.a.b	$1104$	$6$	1104.a	1.a	$1$	$1$	$1$	$177.064$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(9\)	\(-82\)	\(64\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}-82q^{5}+2^{6}q^{7}+3^{4}q^{9}+412q^{11}+\cdots\)
1104.6.a.c	$1104$	$6$	1104.a	1.a	$1$	$1$	$1$	$177.064$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(9\)	\(-44\)	\(70\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}-44q^{5}+70q^{7}+3^{4}q^{9}+136q^{11}+\cdots\)
1104.6.a.d	$1104$	$6$	1104.a	1.a	$1$	$1$	$1$	$177.064$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(9\)	\(-10\)	\(8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}-10q^{5}+8q^{7}+3^{4}q^{9}+300q^{11}+\cdots\)
1104.6.a.e	$1104$	$6$	1104.a	1.a	$1$	$1$	$1$	$177.064$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(9\)	\(76\)	\(-210\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}+76q^{5}-210q^{7}+3^{4}q^{9}+\cdots\)
1104.6.a.f	$1104$	$6$	1104.a	1.a	$1$	$2$	$2$	$177.064$	\(\Q(\sqrt{154}) \)	None	✓	$1$	$0$	\(0\)	\(-18\)	\(-4\)	\(40\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}+(-2+3\beta )q^{5}+(20+5\beta )q^{7}+\cdots\)
1104.6.a.g	$1104$	$6$	1104.a	1.a	$1$	$2$	$2$	$177.064$	\(\Q(\sqrt{514}) \)	None	✓	$1$	$0$	\(0\)	\(18\)	\(40\)	\(100\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}+(20+3\beta )q^{5}+(50-5\beta )q^{7}+\cdots\)
1104.6.a.h	$1104$	$6$	1104.a	1.a	$1$	$2$	$2$	$177.064$	\(\Q(\sqrt{29}) \)	None	✓	$1$	$1$	\(0\)	\(18\)	\(94\)	\(118\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+9q^{3}+(47-\beta )q^{5}+(59-11\beta )q^{7}+\cdots\)
1104.6.a.i	$1104$	$6$	1104.a	1.a	$1$	$3$	$3$	$177.064$	3.3.5333.1	None	✓	$1$	$0$	\(0\)	\(-27\)	\(-56\)	\(114\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-9q^{3}+(-21+4\beta _{1}+3\beta _{2})q^{5}+(33+\cdots)q^{7}+\cdots\)
1104.6.a.j	$1104$	$6$	1104.a	1.a	$1$	$3$	$3$	$177.064$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-27\)	\(-4\)	\(34\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-9q^{3}+(-1+\beta _{1})q^{5}+(11-\beta _{1}+\beta _{2})q^{7}+\cdots\)
1104.6.a.k	$1104$	$6$	1104.a	1.a	$1$	$3$	$3$	$177.064$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(27\)	\(-18\)	\(50\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+9q^{3}+(-6-\beta _{2})q^{5}+(17-\beta _{1}-2\beta _{2})q^{7}+\cdots\)
1104.6.a.l	$1104$	$6$	1104.a	1.a	$1$	$4$	$4$	$177.064$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-36\)	\(-50\)	\(62\)		$-$	$+$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q-9q^{3}+(-13-\beta _{1}-\beta _{2})q^{5}+(15+\cdots)q^{7}+\cdots\)
1104.6.a.m	$1104$	$6$	1104.a	1.a	$1$	$4$	$4$	$177.064$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-36\)	\(54\)	\(-348\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-9q^{3}+(13-\beta _{1})q^{5}+(-87+\beta _{2}+\cdots)q^{7}+\cdots\)
1104.6.a.n	$1104$	$6$	1104.a	1.a	$1$	$4$	$4$	$177.064$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(36\)	\(-122\)	\(-62\)		$-$	$-$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+9q^{3}+(-28+4\beta _{1}+\beta _{3})q^{5}+(-10+\cdots)q^{7}+\cdots\)
1104.6.a.o	$1104$	$6$	1104.a	1.a	$1$	$4$	$4$	$177.064$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(36\)	\(22\)	\(62\)		$-$	$-$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+9q^{3}+(5+\beta _{1}+\beta _{2}-2\beta _{3})q^{5}+(18+\cdots)q^{7}+\cdots\)
1104.6.a.p	$1104$	$6$	1104.a	1.a	$1$	$4$	$4$	$177.064$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(36\)	\(22\)	\(154\)		$-$	$-$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+9q^{3}+(6+\beta _{1}+\beta _{2}-\beta _{3})q^{5}+(39+\cdots)q^{7}+\cdots\)
1104.6.a.q	$1104$	$6$	1104.a	1.a	$1$	$5$	$5$	$177.064$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-45\)	\(16\)	\(134\)		$+$	$+$	$+$	$+$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	\(q-9q^{3}+(3-\beta _{4})q^{5}+(3^{3}+2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1104.6.a.r	$1104$	$6$	1104.a	1.a	$1$	$5$	$5$	$177.064$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-45\)	\(94\)	\(-272\)		$-$	$+$	$-$	$+$	$2^{9}$	$\mathrm{SU}(2)$	\(q-9q^{3}+(19-\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4})q^{5}+\cdots\)
1104.6.a.s	$1104$	$6$	1104.a	1.a	$1$	$6$	$6$	$177.064$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-54\)	\(50\)	\(154\)		$-$	$+$	$+$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q-9q^{3}+(8-\beta _{2})q^{5}+(26+\beta _{4})q^{7}+\cdots\)
1104.6.a.t	$1104$	$6$	1104.a	1.a	$1$	$6$	$6$	$177.064$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(54\)	\(-90\)	\(-50\)		$+$	$-$	$-$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+9q^{3}+(-15+\beta _{5})q^{5}+(-8+\beta _{1}+\cdots)q^{7}+\cdots\)
1104.6.a.u	$1104$	$6$	1104.a	1.a	$1$	$6$	$6$	$177.064$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(54\)	\(-70\)	\(-144\)		$+$	$-$	$-$	$+$	$2^{7}\cdot 3^{3}\cdot 5$	$\mathrm{SU}(2)$	\(q+9q^{3}+(-12+\beta _{1})q^{5}+(-24-\beta _{2}+\cdots)q^{7}+\cdots\)
1104.6.a.v	$1104$	$6$	1104.a	1.a	$1$	$6$	$6$	$177.064$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(54\)	\(22\)	\(-134\)		$-$	$-$	$-$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q+9q^{3}+(4-\beta _{1})q^{5}+(-22-\beta _{4})q^{7}+\cdots\)
1104.6.a.w	$1104$	$6$	1104.a	1.a	$1$	$6$	$6$	$177.064$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(54\)	\(42\)	\(82\)		$+$	$-$	$+$	$-$	$2^{11}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+9q^{3}+(7+\beta _{2})q^{5}+(14-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1104.6.a.x	$1104$	$6$	1104.a	1.a	$1$	$7$	$7$	$177.064$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-63\)	\(-104\)	\(182\)		$+$	$+$	$-$	$-$	$2^{13}$	$\mathrm{SU}(2)$	\(q-9q^{3}+(-15-\beta _{1})q^{5}+(26-\beta _{2}+\cdots)q^{7}+\cdots\)
1104.6.a.y	$1104$	$6$	1104.a	1.a	$1$	$7$	$7$	$177.064$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(63\)	\(80\)	\(-46\)		$+$	$-$	$+$	$-$	$2^{14}\cdot 3$	$\mathrm{SU}(2)$	\(q+9q^{3}+(11+\beta _{2})q^{5}+(-7-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1104.6.a.z	$1104$	$6$	1104.a	1.a	$1$	$8$	$8$	$177.064$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-72\)	\(-4\)	\(-210\)		$+$	$+$	$+$	$+$	$2^{13}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-9q^{3}+(-1+\beta _{1})q^{5}+(-26-\beta _{3}+\cdots)q^{7}+\cdots\)
1104.6.a.ba	$1104$	$6$	1104.a	1.a	$1$	$8$	$8$	$177.064$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-72\)	\(16\)	\(36\)		$+$	$+$	$-$	$-$	$2^{18}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-9q^{3}+(2+\beta _{1})q^{5}+(5+\beta _{2})q^{7}+3^{4}q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(1104))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(1104)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(552))\)\(^{\oplus 2}\)