Space of modular forms of level 1452, weight 4, and trivial character

• Label: 1452.4.a
• Level: $1452$
• Weight: $4$
• Character orbit: 1452.a
• Rep. character: $\chi_{1452}(1,\cdot)$
• Character field: $\Q$
• Dimension: $55$
• Newform subspaces: $21$
• Sturm bound: $1056$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1452.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 21 \)
Sturm bound:			\(1056\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1452))\).

	Total	New	Old
Modular forms	828	55	773
Cusp forms	756	55	701
Eisenstein series	72	0	72

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
\(+\)	\(+\)	\(+\)	\(+\)		\(108\)	\(0\)	\(108\)		\(96\)	\(0\)	\(96\)		\(12\)	\(0\)	\(12\)
\(+\)	\(+\)	\(-\)	\(-\)		\(102\)	\(0\)	\(102\)		\(90\)	\(0\)	\(90\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)		\(102\)	\(0\)	\(102\)		\(90\)	\(0\)	\(90\)		\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)		\(108\)	\(0\)	\(108\)		\(96\)	\(0\)	\(96\)		\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(+\)	\(-\)		\(102\)	\(14\)	\(88\)		\(96\)	\(14\)	\(82\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(102\)	\(13\)	\(89\)		\(96\)	\(13\)	\(83\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(102\)	\(16\)	\(86\)		\(96\)	\(16\)	\(80\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(102\)	\(12\)	\(90\)		\(96\)	\(12\)	\(84\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(420\)	\(29\)	\(391\)		\(384\)	\(29\)	\(355\)		\(36\)	\(0\)	\(36\)
Minus space			\(-\)		\(408\)	\(26\)	\(382\)		\(372\)	\(26\)	\(346\)		\(36\)	\(0\)	\(36\)

Trace form

55 * q + 3 * q^3 - 2 * q^5 - 12 * q^7 + 495 * q^9 + 2 * q^13 + 54 * q^15 - 150 * q^17 - 64 * q^19 - 60 * q^21 - 240 * q^23 + 1073 * q^25 + 27 * q^27 + 46 * q^29 + 4 * q^31 + 672 * q^35 + 206 * q^37 - 54 * q^39 - 334 * q^41 + 112 * q^43 - 18 * q^45 - 224 * q^47 + 4147 * q^49 + 66 * q^51 + 406 * q^53 + 552 * q^57 + 940 * q^59 - 1382 * q^61 - 108 * q^63 - 172 * q^65 - 372 * q^67 + 96 * q^69 + 2680 * q^71 - 42 * q^73 - 75 * q^75 + 2556 * q^79 + 4455 * q^81 + 20 * q^83 - 2052 * q^85 + 150 * q^87 - 2182 * q^89 - 3400 * q^91 - 2448 * q^93 - 1864 * q^95 - 1530 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1452))\) 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
1452.4.a.a	$1452$	$4$	1452.a	1.a	$1$	$1$	$1$	$85.671$	\(\Q\)	None	✓				132.4.a.a	$1$	$2$	\(0\)	\(-3\)	\(-12\)	\(-14\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-12q^{5}-14q^{7}+9q^{9}-56q^{13}+\cdots\)
1452.4.a.b	$1452$	$4$	1452.a	1.a	$1$	$1$	$1$	$85.671$	\(\Q\)	None	✓				132.4.a.b	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{7}+9q^{9}+88q^{13}+66q^{17}+\cdots\)
1452.4.a.c	$1452$	$4$	1452.a	1.a	$1$	$1$	$1$	$85.671$	\(\Q\)	None	✓				132.4.a.c	$1$	$0$	\(0\)	\(-3\)	\(22\)	\(20\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+22q^{5}+20q^{7}+9q^{9}-22q^{13}+\cdots\)
1452.4.a.d	$1452$	$4$	1452.a	1.a	$1$	$1$	$1$	$85.671$	\(\Q\)	None	✓				12.4.a.a	$1$	$1$	\(0\)	\(3\)	\(-18\)	\(-8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-18q^{5}-8q^{7}+9q^{9}+10q^{13}+\cdots\)
1452.4.a.e	$1452$	$4$	1452.a	1.a	$1$	$1$	$1$	$85.671$	\(\Q\)	None	✓	✓			1452.4.a.e	$1$	$1$	\(0\)	\(3\)	\(-9\)	\(-20\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-9q^{5}-20q^{7}+9q^{9}+37q^{13}+\cdots\)
1452.4.a.f	$1452$	$4$	1452.a	1.a	$1$	$1$	$1$	$85.671$	\(\Q\)	None	✓	✓			1452.4.a.e	$1$	$1$	\(0\)	\(3\)	\(-9\)	\(20\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-9q^{5}+20q^{7}+9q^{9}-37q^{13}+\cdots\)
1452.4.a.g	$1452$	$4$	1452.a	1.a	$1$	$1$	$1$	$85.671$	\(\Q\)	None	✓	✓			1452.4.a.g	$1$	$1$	\(0\)	\(3\)	\(4\)	\(-19\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+4q^{5}-19q^{7}+9q^{9}+54q^{13}+\cdots\)
1452.4.a.h	$1452$	$4$	1452.a	1.a	$1$	$1$	$1$	$85.671$	\(\Q\)	None	✓	✓			1452.4.a.g	$1$	$1$	\(0\)	\(3\)	\(4\)	\(19\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+4q^{5}+19q^{7}+9q^{9}-54q^{13}+\cdots\)
1452.4.a.i	$1452$	$4$	1452.a	1.a	$1$	$1$	$1$	$85.671$	\(\Q\)	None	✓				132.4.a.d	$1$	$1$	\(0\)	\(3\)	\(10\)	\(-8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+10q^{5}-8q^{7}+9q^{9}-18q^{13}+\cdots\)
1452.4.a.j	$1452$	$4$	1452.a	1.a	$1$	$2$	$2$	$85.671$	\(\Q(\sqrt{553}) \)	None	✓	✓			1452.4.a.j	$1$	$0$	\(0\)	\(-6\)	\(-5\)	\(-21\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-2-\beta )q^{5}+(-11+\beta )q^{7}+\cdots\)
1452.4.a.k	$1452$	$4$	1452.a	1.a	$1$	$2$	$2$	$85.671$	\(\Q(\sqrt{553}) \)	None	✓	✓			1452.4.a.j	$1$	$0$	\(0\)	\(-6\)	\(-5\)	\(21\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-2-\beta )q^{5}+(11-\beta )q^{7}+\cdots\)
1452.4.a.l	$1452$	$4$	1452.a	1.a	$1$	$2$	$2$	$85.671$	\(\Q(\sqrt{5}) \)	None	✓				132.4.i.a	$1$	$1$	\(0\)	\(-6\)	\(1\)	\(-22\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-5+11\beta )q^{5}+(-13+4\beta )q^{7}+\cdots\)
1452.4.a.m	$1452$	$4$	1452.a	1.a	$1$	$2$	$2$	$85.671$	\(\Q(\sqrt{5}) \)	None	✓				132.4.i.a	$1$	$0$	\(0\)	\(-6\)	\(1\)	\(22\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-5+11\beta )q^{5}+(13-4\beta )q^{7}+\cdots\)
1452.4.a.n	$1452$	$4$	1452.a	1.a	$1$	$2$	$2$	$85.671$	\(\Q(\sqrt{93}) \)	None	✓	✓			1452.4.a.n	$2$	$1$	\(0\)	\(-6\)	\(12\)	\(0\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-3q^{3}+6q^{5}+\beta q^{7}+9q^{9}-2\beta q^{13}+\cdots\)
1452.4.a.o	$1452$	$4$	1452.a	1.a	$1$	$4$	$4$	$85.671$	4.4.885025.1	None	✓				132.4.i.b	$1$	$1$	\(0\)	\(-12\)	\(-6\)	\(-11\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+(1+\beta _{1}+6\beta _{3})q^{5}+(-2-3\beta _{2}+\cdots)q^{7}+\cdots\)
1452.4.a.p	$1452$	$4$	1452.a	1.a	$1$	$4$	$4$	$85.671$	4.4.885025.1	None	✓		✓		132.4.i.b	$1$	$0$	\(0\)	\(-12\)	\(-6\)	\(11\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+(1+\beta _{1}+6\beta _{3})q^{5}+(2+3\beta _{2}+\cdots)q^{7}+\cdots\)
1452.4.a.q	$1452$	$4$	1452.a	1.a	$1$	$4$	$4$	$85.671$	4.4.20959101.1	None	✓	✓			1452.4.a.q	$2$	$0$	\(0\)	\(12\)	\(12\)	\(0\)		$-$	$-$	$+$	$+$	$2^{5}\cdot 3$	$\mathrm{SU}(2)$	\(q+3q^{3}+(3+\beta _{3})q^{5}-\beta _{1}q^{7}+9q^{9}+\cdots\)
1452.4.a.r	$1452$	$4$	1452.a	1.a	$1$	$6$	$6$	$85.671$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓	✓		1452.4.a.r	$2$	$1$	\(0\)	\(-18\)	\(-12\)	\(0\)		$-$	$+$	$+$	$-$	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-2-\beta _{4})q^{5}+(2\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
1452.4.a.s	$1452$	$4$	1452.a	1.a	$1$	$6$	$6$	$85.671$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	✓			1452.4.a.s	$2$	$0$	\(0\)	\(18\)	\(-12\)	\(0\)		$-$	$-$	$+$	$+$	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-2-\beta _{4})q^{5}+(-\beta _{1}+\beta _{5})q^{7}+\cdots\)
1452.4.a.t	$1452$	$4$	1452.a	1.a	$1$	$6$	$6$	$85.671$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓		✓		132.4.i.c	$1$	$1$	\(0\)	\(18\)	\(13\)	\(-23\)		$-$	$-$	$-$	$-$	$2^{2}\cdot 11$	$\mathrm{SU}(2)$	\(q+3q^{3}+(2-\beta _{2})q^{5}+(-4+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
1452.4.a.u	$1452$	$4$	1452.a	1.a	$1$	$6$	$6$	$85.671$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓				132.4.i.c	$1$	$0$	\(0\)	\(18\)	\(13\)	\(23\)		$-$	$-$	$+$	$+$	$2^{2}\cdot 11$	$\mathrm{SU}(2)$	\(q+3q^{3}+(2-\beta _{2})q^{5}+(4-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1452))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1452)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 2}\)