Space of modular forms of level 2550, weight 2, and Character 2550.d

• Label: 2550.2.d
• Level: $2550$
• Weight: $2$
• Character orbit: 2550.d
• Rep. character: $\chi_{2550}(2449,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $22$
• Sturm bound: $1080$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2550.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 22 \)
Sturm bound:			\(1080\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2550, [\chi])\).

	Total	New	Old
Modular forms	564	48	516
Cusp forms	516	48	468
Eisenstein series	48	0	48

Trace form

48 * q - 48 * q^4 + 4 * q^6 - 48 * q^9 - 16 * q^11 + 16 * q^14 + 48 * q^16 + 8 * q^21 - 4 * q^24 - 16 * q^26 - 32 * q^29 + 16 * q^31 - 8 * q^34 + 48 * q^36 - 8 * q^39 + 32 * q^41 + 16 * q^44 - 48 * q^49 + 4 * q^51 - 4 * q^54 - 16 * q^56 - 16 * q^59 - 48 * q^64 - 8 * q^69 + 16 * q^74 - 16 * q^79 + 48 * q^81 - 8 * q^84 + 32 * q^86 + 64 * q^89 + 48 * q^91 + 32 * q^94 + 4 * q^96 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(2550, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2550.2.d.a	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None		✓			2550.2.a.h	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+3 i q^{7}+\cdots\)
2550.2.d.b	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None					510.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-i q^{3}-q^{4}-q^{6}+4 i q^{7}+\cdots\)
2550.2.d.c	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None		✓			2550.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+i q^{7}+\cdots\)
2550.2.d.d	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None		✓			2550.2.a.m	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-i q^{3}-q^{4}-q^{6}+i q^{7}+\cdots\)
2550.2.d.e	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None		✓			2550.2.a.p	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-i q^{3}-q^{4}-q^{6}+4 i q^{7}+\cdots\)
2550.2.d.f	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None					510.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+2 i q^{7}+\cdots\)
2550.2.d.g	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None					102.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-i q^{3}-q^{4}-q^{6}+2 i q^{7}+\cdots\)
2550.2.d.h	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None		✓			2550.2.a.q	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-i q^{3}-q^{4}-q^{6}+4 i q^{7}+\cdots\)
2550.2.d.i	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None		✓			2550.2.a.k	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+i q^{7}+\cdots\)
2550.2.d.j	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None					510.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}+2 i q^{7}+\cdots\)
2550.2.d.k	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None					510.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}-q^{4}-q^{6}-i q^{8}+\cdots\)
2550.2.d.l	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None		✓			2550.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+q^{6}+3 i q^{7}+\cdots\)
2550.2.d.m	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None					102.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+q^{6}+i q^{8}+\cdots\)
2550.2.d.n	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None					510.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+q^{6}+2 i q^{7}+\cdots\)
2550.2.d.o	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None		✓			2550.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+q^{6}+3 i q^{7}+\cdots\)
2550.2.d.p	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None		✓			2550.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+q^{6}+5 i q^{7}+\cdots\)
2550.2.d.q	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None					102.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+q^{6}+2 i q^{7}+\cdots\)
2550.2.d.r	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None					510.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+q^{6}+2 i q^{7}+\cdots\)
2550.2.d.s	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None					510.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+q^{6}+i q^{8}+\cdots\)
2550.2.d.t	$2550$	$2$	2550.d	5.b	$2$	$2$	$2$	$20.362$	\(\Q(\sqrt{-1}) \)	None		✓			2550.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}-q^{4}+q^{6}-i q^{8}+\cdots\)
2550.2.d.u	$2550$	$2$	2550.d	5.b	$2$	$4$	$4$	$20.362$	\(\Q(i, \sqrt{6})\)	None					510.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+q^{6}+\beta _{2}q^{7}+\cdots\)
2550.2.d.v	$2550$	$2$	2550.d	5.b	$2$	$4$	$4$	$20.362$	\(\Q(i, \sqrt{33})\)	None		✓			2550.2.a.bg	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2550, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2550, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(425, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(510, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(850, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1275, [\chi])\)\(^{\oplus 2}\)