Space of modular forms of level 156, weight 2, and Character 156.k

• Label: 156.2.k
• Level: $156$
• Weight: $2$
• Character orbit: 156.k
• Rep. character: $\chi_{156}(31,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $28$
• Newform subspaces: $6$
• Sturm bound: $56$
• Trace bound: $6$

Defining parameters

Level:	$N$	$=$	$156 = 2^{2} \cdot 3 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	156.k (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$52$
Character field:			$\Q(i)$
Newform subspaces:			$6$
Sturm bound:			$56$
Trace bound:			$6$
Distinguishing $T_p$:			$5$, $7$, $11$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(156, [\chi])$.

	Total	New	Old
Modular forms	64	28	36
Cusp forms	48	28	20
Eisenstein series	16	0	16

Trace form

28 * q + 4 * q^5 - 28 * q^9 + 32 * q^14 + 8 * q^16 + 4 * q^20 - 8 * q^21 - 48 * q^22 - 12 * q^24 - 20 * q^26 - 32 * q^28 + 20 * q^32 - 24 * q^34 + 12 * q^37 - 32 * q^40 - 4 * q^41 + 24 * q^42 + 4 * q^44 - 4 * q^45 + 24 * q^46 + 32 * q^48 + 56 * q^50 - 16 * q^52 - 24 * q^53 - 24 * q^57 - 8 * q^58 + 44 * q^60 + 8 * q^61 - 36 * q^65 + 8 * q^66 + 24 * q^68 - 56 * q^70 + 76 * q^73 - 24 * q^74 - 48 * q^76 - 4 * q^78 + 4 * q^80 + 28 * q^81 + 8 * q^85 + 48 * q^86 - 52 * q^89 - 48 * q^92 + 8 * q^93 + 32 * q^94 + 40 * q^96 + 12 * q^97 - 40 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(156, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
156.2.k.a	$156$	$2$	156.k	52.f	$4$	$2$	$1$	$1.246$	$\Q(\sqrt{-1})$	None		✓			156.2.k.a	$2$	$0$	$-2$	$0$	$-2$	$-4$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}-i q^{3}+2 i q^{4}+(-i-1)q^{5}+\cdots$
156.2.k.b	$156$	$2$	156.k	52.f	$4$	$2$	$1$	$1.246$	$\Q(\sqrt{-1})$	None		✓			156.2.k.a	$2$	$0$	$-2$	$0$	$-2$	$4$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i-1)q^{2}+i q^{3}+2 i q^{4}+(-i-1)q^{5}+\cdots$
156.2.k.c	$156$	$2$	156.k	52.f	$4$	$2$	$1$	$1.246$	$\Q(\sqrt{-1})$	None		✓			156.2.k.c	$2$	$0$	$-2$	$0$	$4$	$0$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(i-1)q^{2}+i q^{3}-2 i q^{4}+(2 i+2)q^{5}+\cdots$
156.2.k.d	$156$	$2$	156.k	52.f	$4$	$2$	$1$	$1.246$	$\Q(\sqrt{-1})$	None		✓			156.2.k.c	$2$	$0$	$2$	$0$	$4$	$0$	$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-i+1)q^{2}-i q^{3}-2 i q^{4}+(2 i+2)q^{5}+\cdots$
156.2.k.e	$156$	$2$	156.k	52.f	$4$	$10$	$5$	$1.246$	10.0.$\cdots$.1	None		✓			156.2.k.e	$2$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{2}+\beta _{8}q^{3}+(\beta _{5}+\beta _{7})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$
156.2.k.f	$156$	$2$	156.k	52.f	$4$	$10$	$5$	$1.246$	10.0.$\cdots$.1	None		✓			156.2.k.e	$2$	$0$	$4$	$0$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{3}q^{2}+\beta _{6}q^{3}+(-\beta _{7}-\beta _{8})q^{4}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(156, [\chi])$ into lower level spaces

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