Space of modular forms of level 1100, weight 2, and trivial character

• Label: 1100.2.a
• Level: $1100$
• Weight: $2$
• Character orbit: 1100.a
• Rep. character: $\chi_{1100}(1,\cdot)$
• Character field: $\Q$
• Dimension: $17$
• Newform subspaces: $10$
• Sturm bound: $360$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(360\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1100))\).

	Total	New	Old
Modular forms	198	17	181
Cusp forms	163	17	146
Eisenstein series	35	0	35

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
\(+\)	\(+\)	\(+\)	\(+\)		\(21\)	\(0\)	\(21\)		\(16\)	\(0\)	\(16\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(30\)	\(0\)	\(30\)		\(24\)	\(0\)	\(24\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(27\)	\(0\)	\(27\)		\(21\)	\(0\)	\(21\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(24\)	\(0\)	\(24\)		\(18\)	\(0\)	\(18\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(24\)	\(4\)	\(20\)		\(21\)	\(4\)	\(17\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)		\(24\)	\(3\)	\(21\)		\(21\)	\(3\)	\(18\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)		\(24\)	\(4\)	\(20\)		\(21\)	\(4\)	\(17\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)		\(24\)	\(6\)	\(18\)		\(21\)	\(6\)	\(15\)		\(3\)	\(0\)	\(3\)
Plus space			\(+\)		\(93\)	\(7\)	\(86\)		\(76\)	\(7\)	\(69\)		\(17\)	\(0\)	\(17\)
Minus space			\(-\)		\(105\)	\(10\)	\(95\)		\(87\)	\(10\)	\(77\)		\(18\)	\(0\)	\(18\)

Trace form

17 * q - q^3 + 2 * q^7 + 24 * q^9 + q^11 + 8 * q^13 - 2 * q^17 + 12 * q^19 + 10 * q^21 + 3 * q^23 + 5 * q^27 - 16 * q^29 - 5 * q^31 - 3 * q^33 + 5 * q^37 - 24 * q^41 - 2 * q^43 - 16 * q^47 + 41 * q^49 - 6 * q^51 + 10 * q^53 - 8 * q^57 - 3 * q^59 + 16 * q^61 + 8 * q^63 + 9 * q^67 - q^69 + 13 * q^71 + 24 * q^73 - 2 * q^77 - 22 * q^79 + 69 * q^81 - 18 * q^83 - 16 * q^87 - 11 * q^89 - 28 * q^91 + 11 * q^93 - 13 * q^97 + 18 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1100))\) 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
1100.2.a.a	$1100$	$2$	1100.a	1.a	$1$	$1$	$1$	$8.784$	\(\Q\)	None	✓				220.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{9}+q^{11}+4q^{17}-4q^{19}+\cdots\)
1100.2.a.b	$1100$	$2$	1100.a	1.a	$1$	$1$	$1$	$8.784$	\(\Q\)	None	✓				44.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots\)
1100.2.a.c	$1100$	$2$	1100.a	1.a	$1$	$1$	$1$	$8.784$	\(\Q\)	None	✓				220.2.b.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-3q^{9}-q^{11}+6q^{13}+2q^{17}+\cdots\)
1100.2.a.d	$1100$	$2$	1100.a	1.a	$1$	$1$	$1$	$8.784$	\(\Q\)	None	✓				220.2.b.a	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-3q^{9}-q^{11}-6q^{13}-2q^{17}+\cdots\)
1100.2.a.e	$1100$	$2$	1100.a	1.a	$1$	$1$	$1$	$8.784$	\(\Q\)	None	✓				220.2.a.a	$1$	$0$	\(0\)	\(2\)	\(0\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+4q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
1100.2.a.f	$1100$	$2$	1100.a	1.a	$1$	$2$	$2$	$8.784$	\(\Q(\sqrt{13}) \)	None	✓	✓	✓		1100.2.a.f	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(-2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
1100.2.a.g	$1100$	$2$	1100.a	1.a	$1$	$2$	$2$	$8.784$	\(\Q(\sqrt{21}) \)	None	✓	✓	✓		1100.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-3+\beta )q^{7}+(2+\beta )q^{9}-q^{11}+\cdots\)
1100.2.a.h	$1100$	$2$	1100.a	1.a	$1$	$2$	$2$	$8.784$	\(\Q(\sqrt{21}) \)	None	✓	✓	✓		1100.2.a.g	$1$	$0$	\(0\)	\(1\)	\(0\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(3-\beta )q^{7}+(2+\beta )q^{9}-q^{11}+\cdots\)
1100.2.a.i	$1100$	$2$	1100.a	1.a	$1$	$2$	$2$	$8.784$	\(\Q(\sqrt{13}) \)	None	✓	✓			1100.2.a.f	$1$	$0$	\(0\)	\(3\)	\(0\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(2+\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
1100.2.a.j	$1100$	$2$	1100.a	1.a	$1$	$4$	$4$	$8.784$	\(\Q(\sqrt{3}, \sqrt{19})\)	None	✓		✓		220.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{7}+(3+\beta _{3})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1100)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(550))\)\(^{\oplus 2}\)