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	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(4\)
Plus space			\(+\)	\(7\)
Minus space			\(-\)	\(15\)

Trace form

\( 22q - 2q^{3} + 4q^{5} - 4q^{7} + 22q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1104))\) into newform subspaces

Label	Dim.	\(A\)	Field	CM	Traces					A-L signs			$q$-expansion
					\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)		2	3	23
1104.2.a.a	\(1\)	\(8.815\)	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(4\)		\(+\)	\(+\)	\(-\)	\(q-q^{3}-2q^{5}+4q^{7}+q^{9}-2q^{13}+\cdots\)
1104.2.a.b	\(1\)	\(8.815\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(-2\)		\(-\)	\(+\)	\(-\)	\(q-q^{3}-2q^{7}+q^{9}+2q^{13}-2q^{19}+\cdots\)
1104.2.a.c	\(1\)	\(8.815\)	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(2\)		\(-\)	\(+\)	\(-\)	\(q-q^{3}+2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
1104.2.a.d	\(1\)	\(8.815\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(-2\)		\(+\)	\(-\)	\(-\)	\(q+q^{3}-2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
1104.2.a.e	\(1\)	\(8.815\)	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(2\)		\(-\)	\(-\)	\(-\)	\(q+q^{3}-2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
1104.2.a.f	\(1\)	\(8.815\)	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(2\)		\(+\)	\(-\)	\(+\)	\(q+q^{3}+2q^{7}+q^{9}+2q^{13}+8q^{17}+\cdots\)
1104.2.a.g	\(1\)	\(8.815\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)		\(-\)	\(-\)	\(-\)	\(q+q^{3}+2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
1104.2.a.h	\(1\)	\(8.815\)	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(4\)		\(+\)	\(-\)	\(+\)	\(q+q^{3}+2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
1104.2.a.i	\(1\)	\(8.815\)	\(\Q\)	None	\(0\)	\(1\)	\(4\)	\(-2\)		\(+\)	\(-\)	\(+\)	\(q+q^{3}+4q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots\)
1104.2.a.j	\(2\)	\(8.815\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(-2\)	\(-2\)	\(0\)		\(-\)	\(+\)	\(+\)	\(q-q^{3}+(-1-\beta )q^{5}-2\beta q^{7}+q^{9}+\cdots\)
1104.2.a.k	\(2\)	\(8.815\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(-2\)	\(2\)	\(-4\)		\(+\)	\(+\)	\(+\)	\(q-q^{3}+(1+\beta )q^{5}-2q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
1104.2.a.l	\(2\)	\(8.815\)	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(4\)	\(0\)		\(-\)	\(+\)	\(+\)	\(q-q^{3}+(2+\beta )q^{5}-\beta q^{7}+q^{9}+4\beta q^{11}+\cdots\)
1104.2.a.m	\(2\)	\(8.815\)	\(\Q(\sqrt{5}) \)	None	\(0\)	\(2\)	\(-2\)	\(-2\)		\(-\)	\(-\)	\(+\)	\(q+q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
1104.2.a.n	\(2\)	\(8.815\)	\(\Q(\sqrt{10}) \)	None	\(0\)	\(2\)	\(0\)	\(-4\)		\(-\)	\(-\)	\(-\)	\(q+q^{3}+\beta q^{5}+(-2+\beta )q^{7}+q^{9}+4q^{13}+\cdots\)
1104.2.a.o	\(3\)	\(8.815\)	3.3.148.1	None	\(0\)	\(-3\)	\(0\)	\(-2\)		\(+\)	\(+\)	\(-\)	\(q-q^{3}+\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+q^{9}+\cdots\)

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

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