Space of modular forms of level 4176, weight 2, and Character 4176.o

• Label: 4176.2.o
• Level: $4176$
• Weight: $2$
• Character orbit: 4176.o
• Rep. character: $\chi_{4176}(289,\cdot)$
• Character field: $\Q$
• Dimension: $74$
• Newform subspaces: $19$
• Sturm bound: $1440$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 4176 = 2^{4} \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4176.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(1440\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4176, [\chi])\).

	Total	New	Old
Modular forms	744	76	668
Cusp forms	696	74	622
Eisenstein series	48	2	46

Trace form

\( 74 q + 4 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4176, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4176.2.o.a	$4176$	$2$	4176.o	29.b	$2$	$2$	$2$	$33.346$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-8\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-4q^{5}-q^{7}-5iq^{11}-q^{13}-7iq^{17}+\cdots\)
4176.2.o.b	$4176$	$2$	4176.o	29.b	$2$	$2$	$2$	$33.346$	\(\Q(\sqrt{-13}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{5}-q^{7}+\beta q^{11}-q^{13}-\beta q^{17}+\cdots\)
4176.2.o.c	$4176$	$2$	4176.o	29.b	$2$	$2$	$2$	$33.346$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{5}-3q^{7}+4q^{13}-3iq^{17}+iq^{19}+\cdots\)
4176.2.o.d	$4176$	$2$	4176.o	29.b	$2$	$2$	$2$	$33.346$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{5}+2q^{7}+5iq^{11}-q^{13}-2iq^{17}+\cdots\)
4176.2.o.e	$4176$	$2$	4176.o	29.b	$2$	$2$	$2$	$33.346$	\(\Q(\sqrt{-7}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{5}+2q^{7}-\beta q^{11}+5q^{13}-2\beta q^{17}+\cdots\)
4176.2.o.f	$4176$	$2$	4176.o	29.b	$2$	$2$	$2$	$33.346$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-4iq^{11}-2q^{13}+2iq^{17}+4iq^{19}+\cdots\)
4176.2.o.g	$4176$	$2$	4176.o	29.b	$2$	$2$	$2$	$33.346$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+5q^{7}+iq^{11}+3q^{13}-3iq^{17}+\cdots\)
4176.2.o.h	$4176$	$2$	4176.o	29.b	$2$	$2$	$2$	$33.346$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}-4q^{7}-2iq^{11}+2q^{13}+2iq^{17}+\cdots\)
4176.2.o.i	$4176$	$2$	4176.o	29.b	$2$	$2$	$2$	$33.346$	\(\Q(\sqrt{-13}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}-q^{7}-\beta q^{11}-q^{13}+\beta q^{17}+\cdots\)
4176.2.o.j	$4176$	$2$	4176.o	29.b	$2$	$2$	$2$	$33.346$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}+3q^{7}+3iq^{11}-5q^{13}-3iq^{17}+\cdots\)
4176.2.o.k	$4176$	$2$	4176.o	29.b	$2$	$2$	$2$	$33.346$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{5}-2q^{7}-\beta q^{11}-q^{13}-2\beta q^{17}+\cdots\)
4176.2.o.l	$4176$	$2$	4176.o	29.b	$2$	$4$	$4$	$33.346$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{3})q^{5}+(2+\beta _{3})q^{7}-\beta _{2}q^{11}+\cdots\)
4176.2.o.m	$4176$	$2$	4176.o	29.b	$2$	$4$	$4$	$33.346$	\(\Q(i, \sqrt{13})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}-q^{7}+2\beta _{1}q^{11}+2q^{13}+\cdots\)
4176.2.o.n	$4176$	$2$	4176.o	29.b	$2$	$4$	$4$	$33.346$	\(\Q(i, \sqrt{33})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{5}+(1-\beta _{3})q^{7}-4\beta _{2}q^{11}+\cdots\)
4176.2.o.o	$4176$	$2$	4176.o	29.b	$2$	$4$	$4$	$33.346$	\(\Q(i, \sqrt{33})\)	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2-\beta _{3})q^{5}-3q^{7}+(-\beta _{1}-4\beta _{2}+\cdots)q^{11}+\cdots\)
4176.2.o.p	$4176$	$2$	4176.o	29.b	$2$	$6$	$6$	$33.346$	6.0.\(\cdots\).1	\(\Q(\sqrt{-87}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{3}q^{7}-\beta _{4}q^{11}+\beta _{5}q^{13}+(\beta _{1}-\beta _{4}+\cdots)q^{17}+\cdots\)
4176.2.o.q	$4176$	$2$	4176.o	29.b	$2$	$6$	$6$	$33.346$	6.0.59105344.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(6\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{5}+q^{7}+(-\beta _{2}+\beta _{3})q^{11}+(2+\cdots)q^{13}+\cdots\)
4176.2.o.r	$4176$	$2$	4176.o	29.b	$2$	$8$	$8$	$33.346$	8.0.4589249536.2	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}+(-1+\beta _{6})q^{7}-\beta _{1}q^{11}+\cdots\)
4176.2.o.s	$4176$	$2$	4176.o	29.b	$2$	$16$	$16$	$33.346$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{14}q^{5}+\beta _{12}q^{7}+\beta _{2}q^{11}-\beta _{8}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(4176, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4176, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(174, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(232, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(348, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(464, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(522, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(696, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1044, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1392, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2088, [\chi])\)\(^{\oplus 2}\)