Space of modular forms of level 1100, weight 6, and Character 1100.b

• Label: 1100.6.b
• Level: $1100$
• Weight: $6$
• Character orbit: 1100.b
• Rep. character: $\chi_{1100}(749,\cdot)$
• Character field: $\Q$
• Dimension: $74$
• Newform subspaces: $9$
• Sturm bound: $1080$
• Trace bound: $11$

Defining parameters

Level:	$N$	$=$	$1100 = 2^{2} \cdot 5^{2} \cdot 11$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	1100.b (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$5$
Character field:			$\Q$
Newform subspaces:			$9$
Sturm bound:			$1080$
Trace bound:			$11$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{6}(1100, [\chi])$.

	Total	New	Old
Modular forms	918	74	844
Cusp forms	882	74	808
Eisenstein series	36	0	36

Trace form

74 * q - 4972 * q^9 - 242 * q^11 - 1220 * q^19 - 608 * q^21 + 21004 * q^29 - 10854 * q^31 + 25196 * q^39 + 64908 * q^41 - 186366 * q^49 + 92716 * q^51 - 122934 * q^59 - 40560 * q^61 - 248638 * q^69 + 235342 * q^71 - 56984 * q^79 + 445258 * q^81 + 320274 * q^89 + 125900 * q^91 + 173756 * q^99

Decomposition of $S_{6}^{\mathrm{new}}(1100, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1100.6.b.a	$1100$	$6$	1100.b	5.b	$2$	$2$	$2$	$176.422$	$\Q(\sqrt{-1})$	None					44.6.a.a	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+7 i q^{3}+50 i q^{7}+194 q^{9}+121 q^{11}+\cdots$
1100.6.b.b	$1100$	$6$	1100.b	5.b	$2$	$4$	$4$	$176.422$	$\Q(i, \sqrt{1761})$	None					220.6.a.a	$2$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{1}-5\beta _{2})q^{3}+(5\beta _{1}+34\beta _{2})q^{7}+\cdots$
1100.6.b.c	$1100$	$6$	1100.b	5.b	$2$	$4$	$4$	$176.422$	$\Q(i, \sqrt{31})$	None					44.6.a.b	$2$	$0$	$0$	$0$	$0$	$0$	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-3\beta _{1}+\beta _{3})q^{3}+(-134\beta _{1}+3\beta _{3})q^{7}+\cdots$
1100.6.b.d	$1100$	$6$	1100.b	5.b	$2$	$6$	$6$	$176.422$	$\mathbb{Q}[x]/(x^{6} - \cdots)$	None					220.6.a.b	$2$	$0$	$0$	$0$	$0$	$0$	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{3}+(-24\beta _{3}+7\beta _{4}+2\beta _{5})q^{7}+\cdots$
1100.6.b.e	$1100$	$6$	1100.b	5.b	$2$	$8$	$8$	$176.422$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None					220.6.a.c	$2$	$0$	$0$	$0$	$0$	$0$	$2^{7}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{3}+(-6\beta _{2}+\beta _{4})q^{7}+(-58+\cdots)q^{9}+\cdots$
1100.6.b.f	$1100$	$6$	1100.b	5.b	$2$	$8$	$8$	$176.422$	$\mathbb{Q}[x]/(x^{8} + \cdots)$	None					220.6.a.d	$2$	$0$	$0$	$0$	$0$	$0$	$2^{7}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+(3\beta _{1}-\beta _{2}-\beta _{4})q^{7}+(-58+\cdots)q^{9}+\cdots$
1100.6.b.g	$1100$	$6$	1100.b	5.b	$2$	$10$	$10$	$176.422$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None					220.6.a.e	$2$	$0$	$0$	$0$	$0$	$0$	$2^{12}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{5}q^{3}+(-\beta _{5}+2\beta _{6}+\beta _{8})q^{7}+(-94+\cdots)q^{9}+\cdots$
1100.6.b.h	$1100$	$6$	1100.b	5.b	$2$	$16$	$16$	$176.422$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			1100.6.a.i	$2$	$0$	$0$	$0$	$0$	$0$	$2^{14}\cdot 3^{2}\cdot 5^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{3}+(-2\beta _{8}+4\beta _{9}-\beta _{10})q^{7}+\cdots$
1100.6.b.i	$1100$	$6$	1100.b	5.b	$2$	$16$	$16$	$176.422$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓			1100.6.a.h	$2$	$0$	$0$	$0$	$0$	$0$	$2^{14}\cdot 5^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{8}+\beta _{9})q^{3}+(-2\beta _{9}+\beta _{10})q^{7}+\cdots$

Decomposition of $S_{6}^{\mathrm{old}}(1100, [\chi])$ into lower level spaces

$S_{6}^{\mathrm{old}}(1100, [\chi]) \simeq$ $S_{6}^{\mathrm{new}}(5, [\chi])$$^{\oplus 12}$$\oplus$$S_{6}^{\mathrm{new}}(10, [\chi])$$^{\oplus 8}$$\oplus$$S_{6}^{\mathrm{new}}(20, [\chi])$$^{\oplus 4}$$\oplus$$S_{6}^{\mathrm{new}}(25, [\chi])$$^{\oplus 6}$$\oplus$$S_{6}^{\mathrm{new}}(50, [\chi])$$^{\oplus 4}$$\oplus$$S_{6}^{\mathrm{new}}(55, [\chi])$$^{\oplus 6}$$\oplus$$S_{6}^{\mathrm{new}}(100, [\chi])$$^{\oplus 2}$$\oplus$$S_{6}^{\mathrm{new}}(110, [\chi])$$^{\oplus 4}$$\oplus$$S_{6}^{\mathrm{new}}(220, [\chi])$$^{\oplus 2}$$\oplus$$S_{6}^{\mathrm{new}}(275, [\chi])$$^{\oplus 3}$$\oplus$$S_{6}^{\mathrm{new}}(550, [\chi])$$^{\oplus 2}$