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

• Label: 270.2.c
• Level: $270$
• Weight: $2$
• Character orbit: 270.c
• Rep. character: $\chi_{270}(109,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $108$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(108\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	66	8	58
Cusp forms	42	8	34
Eisenstein series	24	0	24

Trace form

\( 8 q - 8 q^{4} + O(q^{10}) \)

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.c.a	$270$	$2$	270.c	5.b	$2$	$2$	$2$	$2.156$	\(\Q(\sqrt{-1}) \)	None		✓			270.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(-1-2i)q^{5}-4iq^{7}+\cdots\)
270.2.c.b	$270$	$2$	270.c	5.b	$2$	$2$	$2$	$2.156$	\(\Q(\sqrt{-1}) \)	None		✓			270.2.c.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(1-2i)q^{5}+4iq^{7}+\cdots\)
270.2.c.c	$270$	$2$	270.c	5.b	$2$	$4$	$4$	$2.156$	\(\Q(i, \sqrt{19})\)	None		✓	✓		270.2.c.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{4}+\beta _{1}q^{5}+(1+2\beta _{3})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(270, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)