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

\( 100 q - 104 q^{9} - 16 q^{29} + 8 q^{31} - 48 q^{39} + 20 q^{41} - 84 q^{49} + 84 q^{51} + 24 q^{59} - 20 q^{61} - 8 q^{69} + 40 q^{71} + 8 q^{79} + 116 q^{81} + 12 q^{89} - 24 q^{91} - 60 q^{99}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4600.2.e.a	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None					184.2.a.d	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}+2 i q^{7}-6 q^{9}-5 i q^{13}+\cdots\)
4600.2.e.b	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None					920.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 i q^{3}-2 i q^{7}-6 q^{9}-i q^{13}+\cdots\)
4600.2.e.c	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None		✓			4600.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}+i q^{7}-q^{9}-5 q^{11}-i q^{13}+\cdots\)
4600.2.e.d	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None		✓			4600.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}+3 i q^{7}-q^{9}+5 q^{11}+\cdots\)
4600.2.e.e	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None					184.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+2 i q^{7}+2 q^{9}-4 q^{11}+\cdots\)
4600.2.e.f	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None					184.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-4 i q^{7}+2 q^{9}-2 q^{11}+\cdots\)
4600.2.e.g	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None					920.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+2 i q^{7}+2 q^{9}+i q^{13}+\cdots\)
4600.2.e.h	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None					920.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+2 q^{9}+2 q^{11}+5 i q^{13}+\cdots\)
4600.2.e.i	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None		✓			4600.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}-4 i q^{7}+2 q^{9}+3 q^{11}+\cdots\)
4600.2.e.j	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None					920.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{7}+3 q^{9}-6 q^{11}+2 i q^{13}+\cdots\)
4600.2.e.k	$4600$	$2$	4600.e	5.b	$2$	$2$	$2$	$36.731$	\(\Q(\sqrt{-1}) \)	None					184.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+4 i q^{7}+3 q^{9}+6 q^{11}+2 i q^{13}+\cdots\)
4600.2.e.l	$4600$	$2$	4600.e	5.b	$2$	$4$	$4$	$36.731$	\(\Q(i, \sqrt{5})\)	None		✓			4600.2.a.q	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{3}+(-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
4600.2.e.m	$4600$	$2$	4600.e	5.b	$2$	$4$	$4$	$36.731$	\(\Q(i, \sqrt{17})\)	None					920.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-2\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
4600.2.e.n	$4600$	$2$	4600.e	5.b	$2$	$4$	$4$	$36.731$	\(\Q(i, \sqrt{17})\)	None					920.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
4600.2.e.o	$4600$	$2$	4600.e	5.b	$2$	$4$	$4$	$36.731$	\(\Q(i, \sqrt{17})\)	None					184.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-2+\beta _{3})q^{9}+(2-2\beta _{3})q^{11}+\cdots\)
4600.2.e.p	$4600$	$2$	4600.e	5.b	$2$	$6$	$6$	$36.731$	6.0.431642176.2	None					920.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(-3+\beta _{3}+\cdots)q^{9}+\cdots\)
4600.2.e.q	$4600$	$2$	4600.e	5.b	$2$	$6$	$6$	$36.731$	6.0.3356224.1	None					920.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{3}+(-2\beta _{3}-\beta _{5})q^{7}+(-1+\cdots)q^{9}+\cdots\)
4600.2.e.r	$4600$	$2$	4600.e	5.b	$2$	$6$	$6$	$36.731$	6.0.24681024.1	None					920.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)
4600.2.e.s	$4600$	$2$	4600.e	5.b	$2$	$6$	$6$	$36.731$	6.0.153664.1	None		✓			4600.2.a.w	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{5})q^{3}+(-2\beta _{3}-2\beta _{5})q^{7}+\cdots\)
4600.2.e.t	$4600$	$2$	4600.e	5.b	$2$	$8$	$8$	$36.731$	8.0.\(\cdots\).1	None		✓			4600.2.a.ba	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+(-\beta _{1}+\beta _{7})q^{7}+(-2+2\beta _{2}+\cdots)q^{9}+\cdots\)
4600.2.e.u	$4600$	$2$	4600.e	5.b	$2$	$10$	$10$	$36.731$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					920.2.a.j	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{6}+\beta _{8})q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots\)
4600.2.e.v	$4600$	$2$	4600.e	5.b	$2$	$10$	$10$	$36.731$	10.0.\(\cdots\).1	None		✓			4600.2.a.bc	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{2}+\beta _{5})q^{3}+\beta _{8}q^{7}+(-2+\beta _{3}+\cdots)q^{9}+\cdots\)
4600.2.e.w	$4600$	$2$	4600.e	5.b	$2$	$10$	$10$	$36.731$	10.0.\(\cdots\).1	None		✓			4600.2.a.bd	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{4}+\beta _{6})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(4600, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(920, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1150, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2300, [\chi])\)\(^{\oplus 2}\)