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

• Label: 2700.2.i
• Level: $2700$
• Weight: $2$
• Character orbit: 2700.i
• Rep. character: $\chi_{2700}(901,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $38$
• Newform subspaces: $6$
• 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.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
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	38	1150
Cusp forms	972	38	934
Eisenstein series	216	0	216

Trace form

38 * q + q^7 - 5 * q^11 + q^13 - 8 * q^19 + 9 * q^23 + 3 * q^29 + q^31 - 8 * q^37 - 17 * q^41 + q^43 - 15 * q^47 - 24 * q^49 - 36 * q^53 - 7 * q^59 + q^61 + 13 * q^67 - 20 * q^73 - 3 * q^77 + 13 * q^79 + 39 * q^83 + 88 * q^89 - 22 * q^91 + 19 * q^97

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2700.2.i.a	$2700$	$2$	2700.i	9.c	$3$	$2$	$1$	$21.560$	\(\Q(\sqrt{-3}) \)	None					180.2.i.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{7}-4\zeta_{6}q^{13}-6q^{17}+\cdots\)
2700.2.i.b	$2700$	$2$	2700.i	9.c	$3$	$2$	$1$	$21.560$	\(\Q(\sqrt{-3}) \)	None					36.2.e.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}-\zeta_{6}q^{13}+\cdots\)
2700.2.i.c	$2700$	$2$	2700.i	9.c	$3$	$6$	$3$	$21.560$	6.0.954288.1	None					180.2.i.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(3\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{2}-\beta _{4})q^{7}+(\beta _{3}-\beta _{5})q^{11}+(2+\cdots)q^{13}+\cdots\)
2700.2.i.d	$2700$	$2$	2700.i	9.c	$3$	$8$	$4$	$21.560$	8.0.142635249.1	None					900.2.i.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$3^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{7}+(\beta _{1}+\beta _{5})q^{11}+(1+\beta _{1}-\beta _{2}+\cdots)q^{13}+\cdots\)
2700.2.i.e	$2700$	$2$	2700.i	9.c	$3$	$8$	$4$	$21.560$	8.0.142635249.1	None					900.2.i.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$3^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{4}-\beta _{5})q^{7}+(-1-\beta _{1}-\beta _{4}+\cdots)q^{11}+\cdots\)
2700.2.i.f	$2700$	$2$	2700.i	9.c	$3$	$12$	$6$	$21.560$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None			✓		180.2.r.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{3}-\beta _{11})q^{7}+\beta _{2}q^{11}+(-\beta _{7}+\beta _{8}+\cdots)q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2700, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 2}\)