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

• Label: 270.2.i
• Level: $270$
• Weight: $2$
• Character orbit: 270.i
• Rep. character: $\chi_{270}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• 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.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
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	132	12	120
Cusp forms	84	12	72
Eisenstein series	48	0	48

Trace form

12 * q + 6 * q^4 + 2 * q^5 - 8 * q^11 + 10 * q^14 - 6 * q^16 - 2 * q^20 + 6 * q^25 + 24 * q^26 + 6 * q^29 - 12 * q^31 - 32 * q^35 - 26 * q^41 - 16 * q^44 - 12 * q^46 - 4 * q^50 - 24 * q^55 - 10 * q^56 + 4 * q^59 + 6 * q^61 - 12 * q^64 + 36 * q^65 + 6 * q^70 + 24 * q^71 + 28 * q^74 - 24 * q^79 - 4 * q^80 - 12 * q^85 - 28 * q^86 + 68 * q^89 - 24 * q^91 - 6 * q^94 + 36 * q^95

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.i.a	$270$	$2$	270.i	45.j	$6$	$4$	$2$	$2.156$	\(\Q(\zeta_{12})\)	None					90.2.i.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
270.2.i.b	$270$	$2$	270.i	45.j	$6$	$8$	$4$	$2.156$	\(\Q(\zeta_{24})\)	None			✓		90.2.i.b	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta_{4}+\beta_1)q^{2}+(-\beta_{2}+1)q^{4}+\cdots\)

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

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