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

• Label: 468.2.n
• Level: $468$
• Weight: $2$
• Character orbit: 468.n
• Rep. character: $\chi_{468}(307,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $66$
• Newform subspaces: $12$
• Sturm bound: $168$
• Trace bound: $7$

Defining parameters

Level:	$N$	$=$	$468 = 2^{2} \cdot 3^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	468.n (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$52$
Character field:			$\Q(i)$
Newform subspaces:			$12$
Sturm bound:			$168$
Trace bound:			$7$
Distinguishing $T_p$:			$5$, $7$, $11$, $17$

Dimensions

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

	Total	New	Old
Modular forms	184	74	110
Cusp forms	152	66	86
Eisenstein series	32	8	24

Trace form

66 * q + 2 * q^2 + 2 * q^5 + 8 * q^8 - 4 * q^13 - 12 * q^14 + 4 * q^16 - 8 * q^20 + 8 * q^22 + 22 * q^26 - 12 * q^28 + 8 * q^29 - 8 * q^32 + 32 * q^34 + 2 * q^37 - 36 * q^40 + 6 * q^41 + 24 * q^44 - 12 * q^46 - 14 * q^50 - 4 * q^52 + 20 * q^53 + 4 * q^58 - 12 * q^61 + 22 * q^65 - 76 * q^68 - 6 * q^73 - 40 * q^74 - 40 * q^76 - 44 * q^80 + 12 * q^85 - 80 * q^86 + 30 * q^89 + 24 * q^92 - 44 * q^94 - 46 * q^97 + 42 * 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.n.a	$468$	$2$	468.n	52.f	$4$	$2$	$1$	$3.737$	$\Q(\sqrt{-1})$	$\Q(\sqrt{-1})$		✓			468.2.n.a	$4$	$1$	$-2$	$0$	$-6$	$0$	$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i-1)q^{2}+2 i q^{4}+(-3 i-3)q^{5}+\cdots$
468.2.n.b	$468$	$2$	468.n	52.f	$4$	$2$	$1$	$3.737$	$\Q(\sqrt{-1})$	None					156.2.k.c	$2$	$1$	$-2$	$0$	$-4$	$0$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i-1)q^{2}-2 i q^{4}+(-2 i-2)q^{5}+\cdots$
468.2.n.c	$468$	$2$	468.n	52.f	$4$	$2$	$1$	$3.737$	$\Q(\sqrt{-1})$	$\Q(\sqrt{-1})$					52.2.f.a	$4$	$0$	$-2$	$0$	$6$	$0$	$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-i-1)q^{2}+2 i q^{4}+(3 i+3)q^{5}+\cdots$
468.2.n.d	$468$	$2$	468.n	52.f	$4$	$2$	$1$	$3.737$	$\Q(\sqrt{-1})$	None					156.2.k.c	$2$	$0$	$2$	$0$	$-4$	$0$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i+1)q^{2}-2 i q^{4}+(-2 i-2)q^{5}+\cdots$
468.2.n.e	$468$	$2$	468.n	52.f	$4$	$2$	$1$	$3.737$	$\Q(\sqrt{-1})$	None					156.2.k.a	$2$	$0$	$2$	$0$	$2$	$-4$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{2}+2 i q^{4}+(i+1)q^{5}+\cdots$
468.2.n.f	$468$	$2$	468.n	52.f	$4$	$2$	$1$	$3.737$	$\Q(\sqrt{-1})$	None					156.2.k.a	$2$	$0$	$2$	$0$	$2$	$4$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i+1)q^{2}+2 i q^{4}+(i+1)q^{5}+\cdots$
468.2.n.g	$468$	$2$	468.n	52.f	$4$	$2$	$1$	$3.737$	$\Q(\sqrt{-1})$	$\Q(\sqrt{-1})$		✓			468.2.n.a	$4$	$0$	$2$	$0$	$6$	$0$	$1$	$\mathrm{U}(1)[D_{4}]$	$q+(i+1)q^{2}+2 i q^{4}+(3 i+3)q^{5}+\cdots$
468.2.n.h	$468$	$2$	468.n	52.f	$4$	$8$	$4$	$3.737$	8.0.157351936.1	None		✓			468.2.n.h	$8$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots$
468.2.n.i	$468$	$2$	468.n	52.f	$4$	$8$	$4$	$3.737$	8.0.18939904.2	None					52.2.f.b	$4$	$0$	$4$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-\beta _{2}+\beta _{5}-\beta _{7})q^{2}+(-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots$
468.2.n.j	$468$	$2$	468.n	52.f	$4$	$10$	$5$	$3.737$	10.0.$\cdots$.1	None					156.2.k.e	$2$	$0$	$-4$	$0$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{2}+(-\beta _{5}-\beta _{7})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
468.2.n.k	$468$	$2$	468.n	52.f	$4$	$10$	$5$	$3.737$	10.0.$\cdots$.1	None					156.2.k.e	$2$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+(\beta _{7}+\beta _{8})q^{4}+(-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
468.2.n.l	$468$	$2$	468.n	52.f	$4$	$16$	$8$	$3.737$	16.0.$\cdots$.7	None		✓	✓		468.2.n.l	$8$	$0$	$0$	$0$	$0$	$0$	$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{11}q^{2}+\beta _{7}q^{4}-\beta _{2}q^{5}+(\beta _{7}-\beta _{9}+\cdots)q^{7}+\cdots$

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}$