Space of modular forms of level 1332, weight 2, and Character 1332.bi

• Label: 1332.2.bi
• Level: $1332$
• Weight: $2$
• Character orbit: 1332.bi
• Rep. character: $\chi_{1332}(397,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $9$
• Sturm bound: $456$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1332 = 2^{2} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1332.bi (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(456\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1332, [\chi])\).

	Total	New	Old
Modular forms	480	32	448
Cusp forms	432	32	400
Eisenstein series	48	0	48

Trace form

32 * q + q^7 - 8 * q^11 + 3 * q^13 + 9 * q^19 + 28 * q^25 - 45 * q^35 + 23 * q^37 + 18 * q^41 + 20 * q^47 - 9 * q^49 - 17 * q^53 + 21 * q^59 + 24 * q^61 + 19 * q^65 - q^67 - 5 * q^71 + 12 * q^77 + 9 * q^79 + q^83 + 64 * q^85 - 6 * q^89 - 27 * q^91 - 19 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(1332, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1332.2.bi.a	$1332$	$2$	1332.bi	37.e	$6$	$2$	$1$	$10.636$	\(\Q(\sqrt{-3}) \)	None					148.2.h.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{6})q^{5}-\zeta_{6}q^{7}+(2-\zeta_{6})q^{13}+\cdots\)
1332.2.bi.b	$1332$	$2$	1332.bi	37.e	$6$	$2$	$1$	$10.636$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			1332.2.bi.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q-\zeta_{6}q^{7}+(-6+3\zeta_{6})q^{13}+(-4+2\zeta_{6})q^{19}+\cdots\)
1332.2.bi.c	$1332$	$2$	1332.bi	37.e	$6$	$2$	$1$	$10.636$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			1332.2.bi.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(5\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+5\zeta_{6}q^{7}+(2-\zeta_{6})q^{13}+(4-2\zeta_{6})q^{19}+\cdots\)
1332.2.bi.d	$1332$	$2$	1332.bi	37.e	$6$	$2$	$1$	$10.636$	\(\Q(\sqrt{-3}) \)	None					148.2.h.b	$2$	$0$	\(0\)	\(0\)	\(3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{6})q^{5}+2\zeta_{6}q^{7}+(1+\zeta_{6})q^{17}+\cdots\)
1332.2.bi.e	$1332$	$2$	1332.bi	37.e	$6$	$2$	$1$	$10.636$	\(\Q(\sqrt{-3}) \)	None					444.2.r.b	$2$	$0$	\(0\)	\(0\)	\(3\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{6})q^{5}+2\zeta_{6}q^{7}+6q^{11}+(1+\cdots)q^{17}+\cdots\)
1332.2.bi.f	$1332$	$2$	1332.bi	37.e	$6$	$2$	$1$	$10.636$	\(\Q(\sqrt{-3}) \)	None					444.2.r.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(4-2\zeta_{6})q^{5}-\zeta_{6}q^{7}-6q^{11}+(2+\cdots)q^{13}+\cdots\)
1332.2.bi.g	$1332$	$2$	1332.bi	37.e	$6$	$4$	$2$	$10.636$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None					444.2.r.c	$2$	$0$	\(0\)	\(0\)	\(-9\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-3+2\beta _{2}-\beta _{3})q^{5}+(-2+4\beta _{1}+\cdots)q^{7}+\cdots\)
1332.2.bi.h	$1332$	$2$	1332.bi	37.e	$6$	$8$	$4$	$10.636$	8.0.2439569664.7	None		✓			1332.2.bi.h	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{6}q^{5}-\beta _{2}q^{7}+\beta _{4}q^{11}+(1+\beta _{5}+\cdots)q^{13}+\cdots\)
1332.2.bi.i	$1332$	$2$	1332.bi	37.e	$6$	$8$	$4$	$10.636$	8.0.\(\cdots\).1	None					444.2.r.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{5}+(-\beta _{4}-\beta _{7})q^{7}+(-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1332, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1332, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(444, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(666, [\chi])\)\(^{\oplus 2}\)