Space of modular forms of level 1452, weight 2, and trivial character

• Label: 1452.2.a
• Level: $1452$
• Weight: $2$
• Character orbit: 1452.a
• Rep. character: $\chi_{1452}(1,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $13$
• Sturm bound: $528$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1452.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(528\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1452))\).

	Total	New	Old
Modular forms	300	18	282
Cusp forms	229	18	211
Eisenstein series	71	0	71

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(36\)	\(0\)	\(36\)		\(25\)	\(0\)	\(25\)		\(11\)	\(0\)	\(11\)
\(+\)	\(+\)	\(-\)	\(-\)		\(42\)	\(0\)	\(42\)		\(30\)	\(0\)	\(30\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)		\(42\)	\(0\)	\(42\)		\(30\)	\(0\)	\(30\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)		\(36\)	\(0\)	\(36\)		\(24\)	\(0\)	\(24\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(+\)	\(-\)		\(36\)	\(4\)	\(32\)		\(30\)	\(4\)	\(26\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(36\)	\(5\)	\(31\)		\(30\)	\(5\)	\(25\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(36\)	\(2\)	\(34\)		\(30\)	\(2\)	\(28\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(36\)	\(7\)	\(29\)		\(30\)	\(7\)	\(23\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(144\)	\(7\)	\(137\)		\(109\)	\(7\)	\(102\)		\(35\)	\(0\)	\(35\)
Minus space			\(-\)		\(156\)	\(11\)	\(145\)		\(120\)	\(11\)	\(109\)		\(36\)	\(0\)	\(36\)

Trace form

18 * q - 4 * q^5 + 18 * q^9 - 4 * q^13 + 8 * q^19 + 4 * q^21 + 12 * q^23 + 22 * q^25 + 8 * q^29 + 12 * q^31 + 8 * q^39 - 8 * q^41 - 8 * q^43 - 4 * q^45 + 8 * q^47 + 26 * q^49 - 8 * q^51 - 16 * q^53 + 4 * q^57 - 4 * q^59 + 4 * q^61 - 8 * q^65 - 12 * q^67 - 4 * q^69 - 4 * q^71 - 12 * q^73 + 8 * q^75 + 18 * q^81 - 32 * q^83 + 8 * q^87 + 28 * q^89 + 28 * q^91 + 44 * q^93 + 16 * q^95 + 48 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1452))\) 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	11
1452.2.a.a	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	\(\Q\)	None	✓	✓			1452.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}+3q^{13}+q^{15}+\cdots\)
1452.2.a.b	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	\(\Q\)	None	✓	✓			1452.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}-3q^{13}+q^{15}+\cdots\)
1452.2.a.c	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	\(\Q\)	None	✓				132.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}-2q^{7}+q^{9}-6q^{13}+\cdots\)
1452.2.a.d	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	\(\Q\)	None	✓	✓			1452.2.a.d	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(-5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}-5q^{7}+q^{9}-2q^{13}+\cdots\)
1452.2.a.e	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	\(\Q\)	None	✓	✓			1452.2.a.d	$1$	$0$	\(0\)	\(1\)	\(-4\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-4q^{5}+5q^{7}+q^{9}+2q^{13}+\cdots\)
1452.2.a.f	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	\(\Q\)	None	✓				132.2.a.b	$1$	$0$	\(0\)	\(1\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
1452.2.a.g	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	\(\Q\)	None	✓	✓			1452.2.a.g	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-2q^{7}+q^{9}-5q^{13}+\cdots\)
1452.2.a.h	$1452$	$2$	1452.a	1.a	$1$	$1$	$1$	$11.594$	\(\Q\)	None	✓	✓			1452.2.a.g	$1$	$0$	\(0\)	\(1\)	\(3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}+2q^{7}+q^{9}+5q^{13}+\cdots\)
1452.2.a.i	$1452$	$2$	1452.a	1.a	$1$	$2$	$2$	$11.594$	\(\Q(\sqrt{5}) \)	None	✓		✓		132.2.i.b	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-3\beta )q^{5}+(-3+2\beta )q^{7}+\cdots\)
1452.2.a.j	$1452$	$2$	1452.a	1.a	$1$	$2$	$2$	$11.594$	\(\Q(\sqrt{5}) \)	None	✓				132.2.i.b	$1$	$0$	\(0\)	\(-2\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-3\beta )q^{5}+(3-2\beta )q^{7}+q^{9}+\cdots\)
1452.2.a.k	$1452$	$2$	1452.a	1.a	$1$	$2$	$2$	$11.594$	\(\Q(\sqrt{3}) \)	None	✓	✓			1452.2.a.k	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-\beta q^{7}+q^{9}+\beta q^{19}+\beta q^{21}+\cdots\)
1452.2.a.l	$1452$	$2$	1452.a	1.a	$1$	$2$	$2$	$11.594$	\(\Q(\sqrt{5}) \)	None	✓		✓	✓	132.2.i.a	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}+(-3+2\beta )q^{7}+q^{9}+\cdots\)
1452.2.a.m	$1452$	$2$	1452.a	1.a	$1$	$2$	$2$	$11.594$	\(\Q(\sqrt{5}) \)	None	✓		✓		132.2.i.a	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta q^{5}+(3-2\beta )q^{7}+q^{9}+(1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1452))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1452)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 2}\)