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

• Label: 4100.2.d
• Level: $4100$
• Weight: $2$
• Character orbit: 4100.d
• Rep. character: $\chi_{4100}(1149,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $7$
• Sturm bound: $1260$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 4100 = 2^{2} \cdot 5^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4100.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(1260\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	648	60	588
Cusp forms	612	60	552
Eisenstein series	36	0	36

Trace form

\( 60 q - 56 q^{9} + O(q^{10}) \)

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.d.a	$4100$	$2$	4100.d	5.b	$2$	$4$	$4$	$32.739$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+2q^{9}+(-1+\cdots)q^{11}+\cdots\)
4100.2.d.b	$4100$	$2$	4100.d	5.b	$2$	$4$	$4$	$32.739$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(\beta _{1}+\beta _{3})q^{7}+2q^{9}+(3+4\beta _{2}+\cdots)q^{11}+\cdots\)
4100.2.d.c	$4100$	$2$	4100.d	5.b	$2$	$8$	$8$	$32.739$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}-\beta _{4}+\beta _{6})q^{3}+(\beta _{2}-\beta _{4}-\beta _{7})q^{7}+\cdots\)
4100.2.d.d	$4100$	$2$	4100.d	5.b	$2$	$8$	$8$	$32.739$	8.0.4569760000.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{5})q^{7}+(-1+\beta _{4}+\cdots)q^{9}+\cdots\)
4100.2.d.e	$4100$	$2$	4100.d	5.b	$2$	$8$	$8$	$32.739$	8.0.2732361984.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+\beta _{5}q^{7}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
4100.2.d.f	$4100$	$2$	4100.d	5.b	$2$	$14$	$14$	$32.739$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{11}q^{7}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
4100.2.d.g	$4100$	$2$	4100.d	5.b	$2$	$14$	$14$	$32.739$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{7}q^{7}+(\beta _{2}+\beta _{3})q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(4100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(205, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(410, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(820, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1025, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2050, [\chi])\)\(^{\oplus 2}\)