Space of modular forms of level 1104, weight 2, and trivial character

• Label: 1104.2.a
• Level: $1104$
• Weight: $2$
• Character orbit: 1104.a
• Rep. character: $\chi_{1104}(1,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $15$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1104 = 2^{4} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1104.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 15 \)
Sturm bound:			\(384\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1104))\).

	Total	New	Old
Modular forms	204	22	182
Cusp forms	181	22	159
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.

\(2\)	\(3\)	\(23\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(19\)	\(2\)	\(17\)		\(17\)	\(2\)	\(15\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)		\(32\)	\(4\)	\(28\)		\(29\)	\(4\)	\(25\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)		\(23\)	\(3\)	\(20\)		\(20\)	\(3\)	\(17\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)		\(28\)	\(1\)	\(27\)		\(25\)	\(1\)	\(24\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)		\(26\)	\(4\)	\(22\)		\(23\)	\(4\)	\(19\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)		\(25\)	\(2\)	\(23\)		\(22\)	\(2\)	\(20\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)		\(22\)	\(2\)	\(20\)		\(19\)	\(2\)	\(17\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)		\(29\)	\(4\)	\(25\)		\(26\)	\(4\)	\(22\)		\(3\)	\(0\)	\(3\)
Plus space			\(+\)		\(94\)	\(7\)	\(87\)		\(83\)	\(7\)	\(76\)		\(11\)	\(0\)	\(11\)
Minus space			\(-\)		\(110\)	\(15\)	\(95\)		\(98\)	\(15\)	\(83\)		\(12\)	\(0\)	\(12\)

Trace form

22 * q - 2 * q^3 + 4 * q^5 - 4 * q^7 + 22 * q^9 + 4 * q^13 - 4 * q^17 - 4 * q^19 + 26 * q^25 - 2 * q^27 + 4 * q^29 + 8 * q^31 + 8 * q^33 + 24 * q^35 + 4 * q^37 + 4 * q^39 - 4 * q^41 + 12 * q^43 + 4 * q^45 + 24 * q^47 + 22 * q^49 + 20 * q^53 + 32 * q^55 - 8 * q^57 + 32 * q^59 + 20 * q^61 - 4 * q^63 - 24 * q^65 + 20 * q^67 + 32 * q^71 - 20 * q^73 + 2 * q^75 + 16 * q^77 - 28 * q^79 + 22 * q^81 + 8 * q^85 + 12 * q^87 - 20 * q^89 + 24 * q^91 + 24 * q^95 - 20 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1104))\) 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	3	23
1104.2.a.a	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	\(\Q\)	None	✓				552.2.a.e	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+4q^{7}+q^{9}-2q^{13}+\cdots\)
1104.2.a.b	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	\(\Q\)	None	✓				138.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}+q^{9}+2q^{13}-2q^{19}+\cdots\)
1104.2.a.c	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	\(\Q\)	None	✓				69.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
1104.2.a.d	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	\(\Q\)	None	✓		✓	✓	552.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
1104.2.a.e	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	\(\Q\)	None	✓				138.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
1104.2.a.f	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	\(\Q\)	None	✓				552.2.a.b	$1$	$0$	\(0\)	\(1\)	\(0\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{7}+q^{9}+2q^{13}+8q^{17}+\cdots\)
1104.2.a.g	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	\(\Q\)	None	✓				138.2.a.c	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
1104.2.a.h	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	\(\Q\)	None	✓				552.2.a.c	$1$	$0$	\(0\)	\(1\)	\(2\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
1104.2.a.i	$1104$	$2$	1104.a	1.a	$1$	$1$	$1$	$8.815$	\(\Q\)	None	✓				552.2.a.d	$1$	$0$	\(0\)	\(1\)	\(4\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots\)
1104.2.a.j	$1104$	$2$	1104.a	1.a	$1$	$2$	$2$	$8.815$	\(\Q(\sqrt{5}) \)	None	✓				138.2.a.d	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}-2\beta q^{7}+q^{9}+\cdots\)
1104.2.a.k	$1104$	$2$	1104.a	1.a	$1$	$2$	$2$	$8.815$	\(\Q(\sqrt{5}) \)	None	✓		✓	✓	552.2.a.f	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}-2q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
1104.2.a.l	$1104$	$2$	1104.a	1.a	$1$	$2$	$2$	$8.815$	\(\Q(\sqrt{2}) \)	None	✓				276.2.a.b	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(2+\beta )q^{5}-\beta q^{7}+q^{9}+4\beta q^{11}+\cdots\)
1104.2.a.m	$1104$	$2$	1104.a	1.a	$1$	$2$	$2$	$8.815$	\(\Q(\sqrt{5}) \)	None	✓		✓	✓	69.2.a.b	$1$	$1$	\(0\)	\(2\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
1104.2.a.n	$1104$	$2$	1104.a	1.a	$1$	$2$	$2$	$8.815$	\(\Q(\sqrt{10}) \)	None	✓		✓		276.2.a.a	$1$	$0$	\(0\)	\(2\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}+(-2+\beta )q^{7}+q^{9}+4q^{13}+\cdots\)
1104.2.a.o	$1104$	$2$	1104.a	1.a	$1$	$3$	$3$	$8.815$	3.3.148.1	None	✓		✓		552.2.a.g	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(-2\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1104))\) into lower level spaces

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