Space of modular forms of level 468, weight 2, and Character 468.cb

• Label: 468.2.cb
• Level: $468$
• Weight: $2$
• Character orbit: 468.cb
• Rep. character: $\chi_{468}(19,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $132$
• Newform subspaces: $9$
• Sturm bound: $168$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.cb (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(168\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(468, [\chi])\).

	Total	New	Old
Modular forms	368	148	220
Cusp forms	304	132	172
Eisenstein series	64	16	48

Trace form

132 * q + 4 * q^2 - 6 * q^4 + 10 * q^5 - 2 * q^8 - 6 * q^10 - 8 * q^13 + 24 * q^14 - 10 * q^16 + 12 * q^17 + 38 * q^20 + 16 * q^22 + 14 * q^26 + 36 * q^28 + 4 * q^29 + 44 * q^32 - 14 * q^34 - 14 * q^37 + 48 * q^40 + 36 * q^41 - 48 * q^44 + 66 * q^46 - 84 * q^49 - 46 * q^50 - 56 * q^52 + 28 * q^53 - 48 * q^56 + 38 * q^58 + 6 * q^61 - 42 * q^62 + 20 * q^65 + 4 * q^68 - 108 * q^70 - 6 * q^73 - 38 * q^74 - 26 * q^76 - 64 * q^80 - 66 * q^82 - 30 * q^85 - 16 * q^86 - 108 * q^88 - 42 * q^89 - 108 * q^92 - 46 * q^94 + 10 * q^97 - 132 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(468, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
468.2.cb.a	$468$	$2$	468.cb	52.l	$12$	$4$	$1$	$3.737$	\(\Q(\zeta_{12})\)	None					156.2.w.a	$2$	$0$	\(-4\)	\(0\)	\(4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1-\zeta_{12}^{3})q^{2}+2\zeta_{12}^{3}q^{4}+(-2\zeta_{12}+\cdots)q^{5}+\cdots\)
468.2.cb.b	$468$	$2$	468.cb	52.l	$12$	$4$	$1$	$3.737$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		✓			468.2.cb.b	$4$	$0$	\(-2\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
468.2.cb.c	$468$	$2$	468.cb	52.l	$12$	$4$	$1$	$3.737$	\(\Q(\zeta_{12})\)	None					156.2.w.a	$2$	$0$	\(-2\)	\(0\)	\(4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1-\zeta_{12}+\zeta_{12}^{2})q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{4}+\cdots\)
468.2.cb.d	$468$	$2$	468.cb	52.l	$12$	$4$	$1$	$3.737$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)					52.2.l.a	$4$	$0$	\(2\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
468.2.cb.e	$468$	$2$	468.cb	52.l	$12$	$4$	$1$	$3.737$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-1}) \)		✓			468.2.cb.b	$4$	$0$	\(2\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
468.2.cb.f	$468$	$2$	468.cb	52.l	$12$	$16$	$4$	$3.737$	16.0.\(\cdots\).1	None					52.2.l.b	$4$	$0$	\(2\)	\(0\)	\(12\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{12}q^{2}+(\beta _{3}+\beta _{4}+\beta _{8}-\beta _{10}+\beta _{12}+\cdots)q^{4}+\cdots\)
468.2.cb.g	$468$	$2$	468.cb	52.l	$12$	$24$	$6$	$3.737$		None					156.2.w.c	$2$	$0$	\(2\)	\(0\)	\(-2\)	\(2\)		$\mathrm{SU}(2)[C_{12}]$
468.2.cb.h	$468$	$2$	468.cb	52.l	$12$	$24$	$6$	$3.737$		None					156.2.w.c	$2$	$0$	\(4\)	\(0\)	\(-2\)	\(-2\)		$\mathrm{SU}(2)[C_{12}]$
468.2.cb.i	$468$	$2$	468.cb	52.l	$12$	$48$	$12$	$3.737$		None		✓	✓		468.2.cb.i	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(468, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(468, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)