Space of modular forms of level 1850, weight 2, and Character 1850.c

• Label: 1850.2.c
• Level: $1850$
• Weight: $2$
• Character orbit: 1850.c
• Rep. character: $\chi_{1850}(1849,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $12$
• Sturm bound: $570$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(570\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1850, [\chi])\).

	Total	New	Old
Modular forms	296	56	240
Cusp forms	272	56	216
Eisenstein series	24	0	24

Trace form

\( 56 q + 56 q^{4} - 60 q^{9} - 4 q^{11} + 56 q^{16} - 28 q^{26} + 24 q^{34} - 60 q^{36} + 8 q^{41} - 4 q^{44} + 32 q^{46} - 112 q^{49} + 56 q^{64} - 40 q^{71} - 8 q^{74} + 40 q^{81} - 20 q^{86} + 136 q^{99}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1850, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1850.2.c.a	$1850$	$2$	1850.c	185.d	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None					370.2.d.a	$2$	$1$	\(-2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+\beta q^{7}-q^{8}+3 q^{9}+\cdots\)
1850.2.c.b	$1850$	$2$	1850.c	185.d	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None					370.2.d.b	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}+5 i q^{7}-q^{8}+3 q^{9}+\cdots\)
1850.2.c.c	$1850$	$2$	1850.c	185.d	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		✓			1850.2.d.b	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+q^{4}-2 i q^{7}-q^{8}+3 q^{9}+\cdots\)
1850.2.c.d	$1850$	$2$	1850.c	185.d	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None					370.2.d.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-\beta q^{7}+q^{8}+3 q^{9}+\cdots\)
1850.2.c.e	$1850$	$2$	1850.c	185.d	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None					370.2.d.b	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}+5 i q^{7}+q^{8}+3 q^{9}+\cdots\)
1850.2.c.f	$1850$	$2$	1850.c	185.d	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		✓			1850.2.d.b	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+q^{4}-2 i q^{7}+q^{8}+3 q^{9}+\cdots\)
1850.2.c.g	$1850$	$2$	1850.c	185.d	$2$	$4$	$4$	$14.772$	\(\Q(i, \sqrt{21})\)	None					74.2.b.a	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+2\beta _{2}q^{7}+\cdots\)
1850.2.c.h	$1850$	$2$	1850.c	185.d	$2$	$4$	$4$	$14.772$	\(\Q(i, \sqrt{21})\)	None					74.2.b.a	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+2\beta _{2}q^{7}+\cdots\)
1850.2.c.i	$1850$	$2$	1850.c	185.d	$2$	$6$	$6$	$14.772$	6.0.399424.1	None					370.2.d.c	$2$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{5}q^{3}+q^{4}-\beta _{5}q^{6}+(\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
1850.2.c.j	$1850$	$2$	1850.c	185.d	$2$	$6$	$6$	$14.772$	6.0.399424.1	None					370.2.d.c	$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{5}q^{3}+q^{4}+\beta _{5}q^{6}+(\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
1850.2.c.k	$1850$	$2$	1850.c	185.d	$2$	$12$	$12$	$14.772$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1850.2.d.g	$2$	$0$	\(-12\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
1850.2.c.l	$1850$	$2$	1850.c	185.d	$2$	$12$	$12$	$14.772$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1850.2.d.g	$2$	$0$	\(12\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+(-\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1850, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1850, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(925, [\chi])\)\(^{\oplus 2}\)