Space of modular forms of level 2700, weight 2, and Character 2700.s

• Label: 2700.2.s
• Level: $2700$
• Weight: $2$
• Character orbit: 2700.s
• Rep. character: $\chi_{2700}(1549,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $36$
• Newform subspaces: $4$
• Sturm bound: $1080$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2700.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1080\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2700, [\chi])\).

	Total	New	Old
Modular forms	1188	36	1152
Cusp forms	972	36	936
Eisenstein series	216	0	216

Trace form

\( 36 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2700.2.s.a	$2700$	$2$	2700.s	45.j	$6$	$4$	$2$	$21.560$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{7}+(4\zeta_{12}-4\zeta_{12}^{3})q^{13}+6\zeta_{12}^{3}q^{17}+\cdots\)
2700.2.s.b	$2700$	$2$	2700.s	45.j	$6$	$4$	$2$	$21.560$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{7}+(3-3\zeta_{12}^{2})q^{11}+(\zeta_{12}+\cdots)q^{13}+\cdots\)
2700.2.s.c	$2700$	$2$	2700.s	45.j	$6$	$12$	$6$	$21.560$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{3}+\beta _{6})q^{7}+(\beta _{1}+\beta _{8})q^{11}+(\beta _{2}+\cdots)q^{13}+\cdots\)
2700.2.s.d	$2700$	$2$	2700.s	45.j	$6$	$16$	$8$	$21.560$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{10}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{9}q^{7}+(\beta _{2}-\beta _{3})q^{11}+(-\beta _{6}-\beta _{7}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)