Space of modular forms of level 100, weight 11, and Character 100.b

• Label: 100.11.b
• Level: $100$
• Weight: $11$
• Character orbit: 100.b
• Rep. character: $\chi_{100}(51,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $8$
• Sturm bound: $165$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(165\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(100, [\chi])\).

	Total	New	Old
Modular forms	156	98	58
Cusp forms	144	92	52
Eisenstein series	12	6	6

Trace form

\( 92 q - 10 q^{2} + 1238 q^{4} + 10010 q^{6} + 32840 q^{8} - 1682132 q^{9} + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(100, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
100.11.b.a	$100$	$11$	100.b	4.b	$2$	$1$	$1$	$63.536$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(-32\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{5}q^{2}+2^{10}q^{4}-2^{15}q^{8}+3^{10}q^{9}+\cdots\)
100.11.b.b	$100$	$11$	100.b	4.b	$2$	$1$	$1$	$63.536$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(32\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{5}q^{2}+2^{10}q^{4}+2^{15}q^{8}+3^{10}q^{9}+\cdots\)
100.11.b.c	$100$	$11$	100.b	4.b	$2$	$2$	$2$	$63.536$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-5}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-8iq^{2}+59iq^{3}-2^{10}q^{4}+7552q^{6}+\cdots\)
100.11.b.d	$100$	$11$	100.b	4.b	$2$	$4$	$4$	$63.536$	4.0.26777625.2	None		$2$	$0$	\(12\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3-\beta _{1})q^{2}+(2\beta _{1}-\beta _{2})q^{3}+(4-4\beta _{1}+\cdots)q^{4}+\cdots\)
100.11.b.e	$100$	$11$	100.b	4.b	$2$	$20$	$20$	$63.536$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(-22\)	\(0\)	\(0\)	\(0\)	$2^{97}\cdot 3^{4}\cdot 5^{29}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(-2^{5}+\cdots)q^{4}+\cdots\)
100.11.b.f	$100$	$11$	100.b	4.b	$2$	$20$	$20$	$63.536$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(-11\)	\(0\)	\(0\)	\(0\)	$2^{90}\cdot 3^{4}\cdot 5^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(62+\cdots)q^{4}+\cdots\)
100.11.b.g	$100$	$11$	100.b	4.b	$2$	$20$	$20$	$63.536$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(11\)	\(0\)	\(0\)	\(0\)	$2^{90}\cdot 3^{4}\cdot 5^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1})q^{2}+(\beta _{1}-\beta _{2})q^{3}+(62-\beta _{1}+\cdots)q^{4}+\cdots\)
100.11.b.h	$100$	$11$	100.b	4.b	$2$	$24$	$24$	$63.536$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{11}^{\mathrm{old}}(100, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(100, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)