Space of modular forms of level 4100, weight 2, and Character 4100.b

• Label: 4100.2.b
• Level: $4100$
• Weight: $2$
• Character orbit: 4100.b
• Rep. character: $\chi_{4100}(901,\cdot)$
• Character field: $\Q$
• Dimension: $66$
• Newform subspaces: $10$
• Sturm bound: $1260$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 4100 = 2^{2} \cdot 5^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4100.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 41 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1260\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(3\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4100, [\chi])\).

	Total	New	Old
Modular forms	648	66	582
Cusp forms	612	66	546
Eisenstein series	36	0	36

Trace form

\( 66 q - 66 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4100, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4100.2.b.a	$4100$	$2$	4100.b	41.b	$2$	$2$	$2$	$32.739$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-\beta q^{7}+q^{9}-3\beta q^{11}-2\beta q^{17}+\cdots\)
4100.2.b.b	$4100$	$2$	4100.b	41.b	$2$	$2$	$2$	$32.739$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-\beta q^{7}+q^{9}+3\beta q^{11}-2\beta q^{17}+\cdots\)
4100.2.b.c	$4100$	$2$	4100.b	41.b	$2$	$4$	$4$	$32.739$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(\beta _{1}-2\beta _{2})q^{7}+(-1+\beta _{3})q^{9}+\cdots\)
4100.2.b.d	$4100$	$2$	4100.b	41.b	$2$	$4$	$4$	$32.739$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(\beta _{1}-2\beta _{2})q^{7}+(-1+\beta _{3})q^{9}+\cdots\)
4100.2.b.e	$4100$	$2$	4100.b	41.b	$2$	$4$	$4$	$32.739$	4.0.25088.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{7}+\beta _{2}q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
4100.2.b.f	$4100$	$2$	4100.b	41.b	$2$	$6$	$6$	$32.739$	6.0.36433296.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}-\beta _{4}q^{7}+(-2-\beta _{3})q^{9}-\beta _{5}q^{11}+\cdots\)
4100.2.b.g	$4100$	$2$	4100.b	41.b	$2$	$8$	$8$	$32.739$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{3}-\beta _{4}q^{7}+(-1-\beta _{3})q^{9}+\beta _{5}q^{11}+\cdots\)
4100.2.b.h	$4100$	$2$	4100.b	41.b	$2$	$10$	$10$	$32.739$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{9}q^{7}+(-1+\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
4100.2.b.i	$4100$	$2$	4100.b	41.b	$2$	$10$	$10$	$32.739$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{9}q^{7}+(-1+\beta _{2})q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
4100.2.b.j	$4100$	$2$	4100.b	41.b	$2$	$16$	$16$	$32.739$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{3}+\beta _{11}q^{7}+(-1+\beta _{1})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(82, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(205, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(410, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(820, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1025, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2050, [\chi])\)\(^{\oplus 2}\)