Space of modular forms of level 4600, weight 2, and Character 4600.e

• Label: 4600.2.e
• Level: $4600$
• Weight: $2$
• Character orbit: 4600.e
• Rep. character: $\chi_{4600}(4049,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $23$
• Sturm bound: $1440$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4600.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 23 \)
Sturm bound:			\(1440\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4600, [\chi])\).

	Total	New	Old
Modular forms	744	100	644
Cusp forms	696	100	596
Eisenstein series	48	0	48

Trace form

\( 100 q - 104 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4600, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4600.2.e.a	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+2iq^{7}-6q^{9}-5iq^{13}+\cdots\)
4600.2.e.b	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}-2iq^{7}-6q^{9}-iq^{13}+6q^{21}+\cdots\)
4600.2.e.c	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+iq^{7}-q^{9}-5q^{11}-iq^{13}+\cdots\)
4600.2.e.d	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+3iq^{7}-q^{9}+5q^{11}-5iq^{13}+\cdots\)
4600.2.e.e	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{7}+2q^{9}-4q^{11}+5iq^{13}+\cdots\)
4600.2.e.f	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-4iq^{7}+2q^{9}-2q^{11}-7iq^{13}+\cdots\)
4600.2.e.g	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2iq^{7}+2q^{9}+iq^{13}+4iq^{17}+\cdots\)
4600.2.e.h	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2q^{9}+2q^{11}+5iq^{13}-4iq^{17}+\cdots\)
4600.2.e.i	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-4iq^{7}+2q^{9}+3q^{11}-2iq^{13}+\cdots\)
4600.2.e.j	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{7}+3q^{9}-6q^{11}+2iq^{13}-3iq^{17}+\cdots\)
4600.2.e.k	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4iq^{7}+3q^{9}+6q^{11}+2iq^{13}+\cdots\)
4600.2.e.l	$4600$	$2$	4600.e	5.b	$2$	$4$	$4$	$36.731$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{3}+(-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
4600.2.e.m	$4600$	$2$	4600.e	5.b	$2$	$4$	$4$	$36.731$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-2\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
4600.2.e.n	$4600$	$2$	4600.e	5.b	$2$	$4$	$4$	$36.731$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
4600.2.e.o	$4600$	$2$	4600.e	5.b	$2$	$4$	$4$	$36.731$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-2+\beta _{3})q^{9}+(2-2\beta _{3})q^{11}+\cdots\)
4600.2.e.p	$4600$	$2$	4600.e	5.b	$2$	$6$	$6$	$36.731$	6.0.431642176.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(-3+\beta _{3}+\cdots)q^{9}+\cdots\)
4600.2.e.q	$4600$	$2$	4600.e	5.b	$2$	$6$	$6$	$36.731$	6.0.3356224.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{3}+(-2\beta _{3}-\beta _{5})q^{7}+(-1+\cdots)q^{9}+\cdots\)
4600.2.e.r	$4600$	$2$	4600.e	5.b	$2$	$6$	$6$	$36.731$	6.0.24681024.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)
4600.2.e.s	$4600$	$2$	4600.e	5.b	$2$	$6$	$6$	$36.731$	6.0.153664.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{5})q^{3}+(-2\beta _{3}-2\beta _{5})q^{7}+\cdots\)
4600.2.e.t	$4600$	$2$	4600.e	5.b	$2$	$8$	$8$	$36.731$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+(-\beta _{1}+\beta _{7})q^{7}+(-2+2\beta _{2}+\cdots)q^{9}+\cdots\)
4600.2.e.u	$4600$	$2$	4600.e	5.b	$2$	$10$	$10$	$36.731$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{6}+\beta _{8})q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots\)
4600.2.e.v	$4600$	$2$	4600.e	5.b	$2$	$10$	$10$	$36.731$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{2}+\beta _{5})q^{3}+\beta _{8}q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots\)
4600.2.e.w	$4600$	$2$	4600.e	5.b	$2$	$10$	$10$	$36.731$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{4}+\beta _{6})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)