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

• Label: 1452.2.i
• Level: $1452$
• Weight: $2$
• Character orbit: 1452.i
• Rep. character: $\chi_{1452}(493,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $72$
• Newform subspaces: $17$
• 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.i (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(528\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	1200	72	1128
Cusp forms	912	72	840
Eisenstein series	288	0	288

Trace form

72 * q + 4 * q^5 - 10 * q^7 - 18 * q^9 - 6 * q^13 + 10 * q^15 + 10 * q^17 - 8 * q^19 + 16 * q^21 + 28 * q^23 - 12 * q^25 + 12 * q^29 - 12 * q^31 + 20 * q^35 - 10 * q^37 - 8 * q^39 + 28 * q^41 + 8 * q^43 + 4 * q^45 - 18 * q^47 - 16 * q^49 - 12 * q^51 - 14 * q^53 - 24 * q^57 - 26 * q^59 - 14 * q^61 - 10 * q^63 - 52 * q^65 + 52 * q^67 - 6 * q^69 - 36 * q^71 + 12 * q^73 - 8 * q^75 - 10 * q^79 - 18 * q^81 + 2 * q^83 - 30 * q^85 - 8 * q^87 - 28 * q^89 - 38 * q^91 - 24 * q^93 + 14 * q^95 + 2 * q^97

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.i.a	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None		✓			1452.2.a.g	$4$	$0$	\(0\)	\(-1\)	\(-3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}-3\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.b	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None		✓			1452.2.a.g	$4$	$0$	\(0\)	\(-1\)	\(-3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}-3\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.c	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None					132.2.i.a	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}+(-1+\zeta_{10}-\zeta_{10}^{2})q^{5}+\cdots\)
1452.2.i.d	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None					132.2.a.b	$4$	$0$	\(0\)	\(-1\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}-2\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.e	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None					132.2.a.b	$4$	$0$	\(0\)	\(-1\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}-2\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.f	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None					132.2.i.a	$2$	$0$	\(0\)	\(-1\)	\(-2\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}+(-1+\zeta_{10}-\zeta_{10}^{2})q^{5}+\cdots\)
1452.2.i.g	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None					132.2.i.a	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}+(1+\zeta_{10}^{2})q^{5}+(-2+2\zeta_{10}+\cdots)q^{7}+\cdots\)
1452.2.i.h	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None		✓			1452.2.a.d	$4$	$0$	\(0\)	\(-1\)	\(4\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}+4\zeta_{10}q^{5}-5\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.i	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None		✓			1452.2.a.d	$4$	$0$	\(0\)	\(-1\)	\(4\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+\zeta_{10}^{2}q^{3}+4\zeta_{10}q^{5}+5\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.j	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None					132.2.i.b	$2$	$0$	\(0\)	\(1\)	\(-7\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\zeta_{10}^{2}q^{3}+(-3+2\zeta_{10}-3\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
1452.2.i.k	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None					132.2.a.a	$4$	$0$	\(0\)	\(1\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\zeta_{10}^{2}q^{3}-2\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.l	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None					132.2.a.a	$4$	$0$	\(0\)	\(1\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\zeta_{10}^{2}q^{3}-2\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.m	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None		✓			1452.2.a.a	$4$	$0$	\(0\)	\(1\)	\(1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\zeta_{10}^{2}q^{3}+\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.n	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None		✓			1452.2.a.a	$4$	$0$	\(0\)	\(1\)	\(1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\zeta_{10}^{2}q^{3}+\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots\)
1452.2.i.o	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None					132.2.i.b	$2$	$0$	\(0\)	\(1\)	\(8\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\zeta_{10}^{2}q^{3}+(3-\zeta_{10}+3\zeta_{10}^{2})q^{5}+\cdots\)
1452.2.i.p	$1452$	$2$	1452.i	11.c	$5$	$4$	$1$	$11.594$	\(\Q(\zeta_{10})\)	None					132.2.i.b	$2$	$0$	\(0\)	\(1\)	\(8\)	\(7\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\zeta_{10}^{2}q^{3}+(3-\zeta_{10}+3\zeta_{10}^{2})q^{5}+\cdots\)
1452.2.i.q	$1452$	$2$	1452.i	11.c	$5$	$8$	$2$	$11.594$	8.0.324000000.3	None		✓	✓		1452.2.a.k	$8$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1+\beta _{2}+\beta _{4}+\beta _{6})q^{3}+\beta _{7}q^{7}+\beta _{6}q^{9}+\cdots\)

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

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