Space of modular forms of level 1452, weight 2, and Character 1452.b

• Label: 1452.2.b
• Level: $1452$
• Weight: $2$
• Character orbit: 1452.b
• Rep. character: $\chi_{1452}(725,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $5$
• Sturm bound: $528$
• Trace bound: $91$

Defining parameters

Level:	\( N \)	\(=\)	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1452.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(528\)
Trace bound:			\(91\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1452, [\chi])\).

	Total	New	Old
Modular forms	300	36	264
Cusp forms	228	36	192
Eisenstein series	72	0	72

Trace form

\( 36 q - 4 q^{9} + 2 q^{15} - 16 q^{25} + 18 q^{27} + 4 q^{31} - 24 q^{37} + 20 q^{45} - 72 q^{49} - 40 q^{67} - 26 q^{69} - 48 q^{75} + 20 q^{81} - 28 q^{91} + 54 q^{93} + 72 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1452, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1452.2.b.a	$1452$	$2$	1452.b	33.d	$2$	$4$	$4$	$11.594$	\(\Q(\sqrt{-2}, \sqrt{-11})\)	None		✓			1452.2.b.a	$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(-1+2\beta _{3})q^{5}-3\beta _{2}q^{7}+\cdots\)
1452.2.b.b	$1452$	$2$	1452.b	33.d	$2$	$4$	$4$	$11.594$	\(\Q(\sqrt{-2}, \sqrt{3})\)	\(\Q(\sqrt{-3}) \)		✓			1452.2.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{3}+(-2\beta _{1}+\beta _{3})q^{7}+3q^{9}+\cdots\)
1452.2.b.c	$1452$	$2$	1452.b	33.d	$2$	$4$	$4$	$11.594$	\(\Q(\sqrt{-2}, \sqrt{3})\)	\(\Q(\sqrt{-3}) \)		✓			1452.2.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{3}+(2\beta _{1}+\beta _{3})q^{7}+3q^{9}+(-\beta _{1}+\cdots)q^{13}+\cdots\)
1452.2.b.d	$1452$	$2$	1452.b	33.d	$2$	$8$	$8$	$11.594$	8.0.3588489216.5	None		✓			1452.2.b.d	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{3}+\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
1452.2.b.e	$1452$	$2$	1452.b	33.d	$2$	$16$	$16$	$11.594$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓		132.2.p.a	$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+\beta _{15}q^{5}+(\beta _{1}+\beta _{2}+\beta _{14}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1452, [\chi])\) into lower level spaces

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