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

• Label: 2700.2.d
• Level: $2700$
• Weight: $2$
• Character orbit: 2700.d
• Rep. character: $\chi_{2700}(649,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $12$
• Sturm bound: $1080$
• Trace bound: $31$

Defining parameters

Level:	\( N \)	\(=\)	\( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2700.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1080\)
Trace bound:			\(31\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	594	24	570
Cusp forms	486	24	462
Eisenstein series	108	0	108

Trace form

\( 24 q + 6 q^{19} - 6 q^{31} - 66 q^{49} - 18 q^{61} + 36 q^{79} + 78 q^{91}+O(q^{100}) \)

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.d.a	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	\(\Q(\sqrt{-1}) \)	None					540.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{7}-6 q^{11}-i q^{13}+q^{19}-6 i q^{23}+\cdots\)
2700.2.d.b	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	\(\Q(\sqrt{-1}) \)	None					540.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4 i q^{7}-6 q^{11}-4 i q^{13}-3 i q^{17}+\cdots\)
2700.2.d.c	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	\(\Q(\sqrt{-1}) \)	None		✓			2700.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{7}-3 q^{11}+i q^{13}-6 i q^{17}+\cdots\)
2700.2.d.d	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)		✓			2700.2.a.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4 i q^{7}-7 i q^{13}-8 q^{19}-7 q^{31}+\cdots\)
2700.2.d.e	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	\(\Q(\sqrt{-1}) \)	None					540.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{7}-2 i q^{13}+3 i q^{17}-5 q^{19}+\cdots\)
2700.2.d.f	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	\(\Q(\sqrt{-1}) \)	None					540.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{7}-2 i q^{13}-3 i q^{17}-5 q^{19}+\cdots\)
2700.2.d.g	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)					108.2.a.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+5 i q^{7}+7 i q^{13}+q^{19}-4 q^{31}+\cdots\)
2700.2.d.h	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)		✓			2700.2.a.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+5 i q^{7}-2 i q^{13}+q^{19}+11 q^{31}+\cdots\)
2700.2.d.i	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)		✓			2700.2.a.j	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+i q^{7}+2 i q^{13}+7 q^{19}-7 q^{31}+\cdots\)
2700.2.d.j	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	\(\Q(\sqrt{-1}) \)	None		✓			2700.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{7}+3 q^{11}+i q^{13}+6 i q^{17}+\cdots\)
2700.2.d.k	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	\(\Q(\sqrt{-1}) \)	None					540.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{7}+6 q^{11}-i q^{13}+q^{19}+6 i q^{23}+\cdots\)
2700.2.d.l	$2700$	$2$	2700.d	5.b	$2$	$2$	$2$	$21.560$	\(\Q(\sqrt{-1}) \)	None					540.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4 i q^{7}+6 q^{11}-4 i q^{13}+3 i q^{17}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2700, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 2}\)