Space of modular forms of level 2050, weight 2, and Character 2050.c

• Label: 2050.2.c
• Level: $2050$
• Weight: $2$
• Character orbit: 2050.c
• Rep. character: $\chi_{2050}(1149,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $16$
• Sturm bound: $630$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2050 = 2 \cdot 5^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2050.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(630\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2050, [\chi])\).

	Total	New	Old
Modular forms	328	60	268
Cusp forms	304	60	244
Eisenstein series	24	0	24

Trace form

\( 60 q - 60 q^{4} - 4 q^{6} - 68 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2050, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2050.2.c.a	$2050$	$2$	2050.c	5.b	$2$	$2$	$2$	$16.369$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}-2iq^{7}+\cdots\)
2050.2.c.b	$2050$	$2$	2050.c	5.b	$2$	$2$	$2$	$16.369$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+3q^{9}+\cdots\)
2050.2.c.c	$2050$	$2$	2050.c	5.b	$2$	$2$	$2$	$16.369$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+4iq^{7}-iq^{8}+3q^{9}+\cdots\)
2050.2.c.d	$2050$	$2$	2050.c	5.b	$2$	$2$	$2$	$16.369$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+5iq^{7}+iq^{8}+3q^{9}+\cdots\)
2050.2.c.e	$2050$	$2$	2050.c	5.b	$2$	$2$	$2$	$16.369$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}-4iq^{7}+\cdots\)
2050.2.c.f	$2050$	$2$	2050.c	5.b	$2$	$2$	$2$	$16.369$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+2iq^{3}-q^{4}+2q^{6}+2iq^{7}+\cdots\)
2050.2.c.g	$2050$	$2$	2050.c	5.b	$2$	$4$	$4$	$16.369$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-2\beta _{1}q^{3}-q^{4}-2q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
2050.2.c.h	$2050$	$2$	2050.c	5.b	$2$	$4$	$4$	$16.369$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
2050.2.c.i	$2050$	$2$	2050.c	5.b	$2$	$4$	$4$	$16.369$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-1+\beta _{3})q^{6}+\cdots\)
2050.2.c.j	$2050$	$2$	2050.c	5.b	$2$	$4$	$4$	$16.369$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{2}q^{6}+\beta _{3}q^{7}+\cdots\)
2050.2.c.k	$2050$	$2$	2050.c	5.b	$2$	$4$	$4$	$16.369$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}-q^{4}+\beta _{3}q^{6}-2\beta _{1}q^{7}+\cdots\)
2050.2.c.l	$2050$	$2$	2050.c	5.b	$2$	$4$	$4$	$16.369$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\zeta_{8}^{3}q^{6}+\cdots\)
2050.2.c.m	$2050$	$2$	2050.c	5.b	$2$	$4$	$4$	$16.369$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}-q^{4}+(1+\cdots)q^{6}+\cdots\)
2050.2.c.n	$2050$	$2$	2050.c	5.b	$2$	$6$	$6$	$16.369$	6.0.2611456.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+\beta _{2}q^{3}-q^{4}+\beta _{1}q^{6}+2\beta _{4}q^{7}+\cdots\)
2050.2.c.o	$2050$	$2$	2050.c	5.b	$2$	$6$	$6$	$16.369$	6.0.77580864.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{3}q^{6}+\beta _{2}q^{7}+\cdots\)
2050.2.c.p	$2050$	$2$	2050.c	5.b	$2$	$8$	$8$	$16.369$	8.0.7718676736.7	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}+(\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2050, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2050, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(205, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(410, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1025, [\chi])\)\(^{\oplus 2}\)