Space of modular forms of level 1452, weight 3, and Character 1452.e

• Label: 1452.3.e
• Level: $1452$
• Weight: $3$
• Character orbit: 1452.e
• Rep. character: $\chi_{1452}(485,\cdot)$
• Character field: $\Q$
• Dimension: $73$
• Newform subspaces: $13$
• Sturm bound: $792$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1452.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(792\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1452, [\chi])\).

	Total	New	Old
Modular forms	564	73	491
Cusp forms	492	73	419
Eisenstein series	72	0	72

Trace form

\( 73 q + 3 q^{3} - 6 q^{7} + 7 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1452, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1452.3.e.a	$1452$	$3$	1452.e	3.b	$2$	$1$	$1$	$39.564$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-13\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}-13q^{7}+9q^{9}-22q^{13}-37q^{19}+\cdots\)
1452.3.e.b	$1452$	$3$	1452.e	3.b	$2$	$1$	$1$	$39.564$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-2\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}-2q^{7}+9q^{9}+22q^{13}-26q^{19}+\cdots\)
1452.3.e.c	$1452$	$3$	1452.e	3.b	$2$	$1$	$1$	$39.564$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(13\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}+13q^{7}+9q^{9}+22q^{13}+37q^{19}+\cdots\)
1452.3.e.d	$1452$	$3$	1452.e	3.b	$2$	$2$	$2$	$39.564$	\(\Q(\sqrt{-11}) \)	None		$2$	$0$	\(0\)	\(5\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3-\beta )q^{3}+(1-2\beta )q^{5}-2q^{7}+(6+\cdots)q^{9}+\cdots\)
1452.3.e.e	$1452$	$3$	1452.e	3.b	$2$	$2$	$2$	$39.564$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-3}) \)	✓	$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{3}-3\beta q^{7}+9q^{9}+8\beta q^{13}-5\beta q^{19}+\cdots\)
1452.3.e.f	$1452$	$3$	1452.e	3.b	$2$	$2$	$2$	$39.564$	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-3}) \)	✓	$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{3}+\beta q^{7}+9q^{9}+\beta q^{13}-2\beta q^{19}+\cdots\)
1452.3.e.g	$1452$	$3$	1452.e	3.b	$2$	$4$	$4$	$39.564$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)		$4$	$0$	\(0\)	\(-5\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1+\beta _{2})q^{3}+\beta _{3}q^{5}+(-3-2\beta _{1}+\cdots)q^{9}+\cdots\)
1452.3.e.h	$1452$	$3$	1452.e	3.b	$2$	$4$	$4$	$39.564$	\(\Q(\sqrt{-2}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{3}+(\beta _{1}-\beta _{3})q^{5}+\beta _{2}q^{7}+\cdots\)
1452.3.e.i	$1452$	$3$	1452.e	3.b	$2$	$6$	$6$	$39.564$	6.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-16\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}+(-2-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1452.3.e.j	$1452$	$3$	1452.e	3.b	$2$	$6$	$6$	$39.564$	6.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(16\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1})q^{3}+\beta _{2}q^{5}+(2+\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
1452.3.e.k	$1452$	$3$	1452.e	3.b	$2$	$12$	$12$	$39.564$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{3}\cdot 3^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}-\beta _{8}q^{5}+(2\beta _{1}+\beta _{6}-\beta _{7}+\cdots)q^{7}+\cdots\)
1452.3.e.l	$1452$	$3$	1452.e	3.b	$2$	$16$	$16$	$39.564$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{12}q^{3}+\beta _{10}q^{5}+\beta _{5}q^{7}+(1-\beta _{11}+\cdots)q^{9}+\cdots\)
1452.3.e.m	$1452$	$3$	1452.e	3.b	$2$	$16$	$16$	$39.564$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{12}q^{3}+\beta _{10}q^{5}-\beta _{5}q^{7}+(1-\beta _{11}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1452, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1452, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(726, [\chi])\)\(^{\oplus 2}\)