Space of modular forms of level 270, weight 2, and Character 270.m

• Label: 270.2.m
• Level: $270$
• Weight: $2$
• Character orbit: 270.m
• Rep. character: $\chi_{270}(17,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $108$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$270 = 2 \cdot 3^{3} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	270.m (of order $12$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$45$
Character field:			$\Q(\zeta_{12})$
Newform subspaces:			$2$
Sturm bound:			$108$
Trace bound:			$1$
Distinguishing $T_p$:			$7$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(270, [\chi])$.

	Total	New	Old
Modular forms	264	24	240
Cusp forms	168	24	144
Eisenstein series	96	0	96

Trace form

24 * q + 24 * q^11 + 12 * q^16 + 12 * q^20 + 24 * q^23 - 12 * q^25 - 24 * q^37 - 36 * q^38 - 36 * q^41 - 24 * q^46 - 48 * q^47 - 48 * q^50 - 24 * q^55 - 12 * q^56 + 12 * q^58 - 12 * q^61 + 24 * q^65 - 12 * q^67 + 36 * q^68 + 48 * q^77 - 48 * q^82 - 60 * q^83 - 24 * q^85 + 72 * q^86 + 48 * q^91 + 24 * q^92 - 60 * q^95 - 36 * q^97

Decomposition of $S_{2}^{\mathrm{new}}(270, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
270.2.m.a	$270$	$2$	270.m	45.l	$12$	$8$	$2$	$2.156$	$\Q(\zeta_{24})$	None					90.2.l.a	$4$	$0$	$0$	$0$	$-12$	$-8$	$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-1+\zeta_{24}^{3}+\cdots)q^{5}+\cdots$
270.2.m.b	$270$	$2$	270.m	45.l	$12$	$16$	$4$	$2.156$	16.0.$\cdots$.9	None			✓		90.2.l.b	$4$	$0$	$0$	$0$	$12$	$8$	$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\beta _{5}q^{2}-\beta _{6}q^{4}+(-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(270, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(270, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(45, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(90, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(135, [\chi])$$^{\oplus 2}$