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

• Label: 1850.2.b
• Level: $1850$
• Weight: $2$
• Character orbit: 1850.b
• Rep. character: $\chi_{1850}(149,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $16$
• Sturm bound: $570$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(570\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	298	54	244
Cusp forms	274	54	220
Eisenstein series	24	0	24

Trace form

54 * q - 54 * q^4 + 4 * q^6 - 78 * q^9 + 8 * q^11 + 54 * q^16 + 20 * q^19 + 8 * q^21 - 4 * q^24 + 4 * q^29 - 8 * q^31 + 78 * q^36 + 24 * q^39 + 8 * q^41 - 8 * q^44 + 24 * q^46 - 30 * q^49 - 28 * q^51 + 20 * q^54 + 8 * q^59 + 20 * q^61 - 54 * q^64 - 28 * q^66 + 72 * q^69 - 8 * q^71 + 10 * q^74 - 20 * q^76 + 16 * q^79 + 134 * q^81 - 8 * q^84 - 28 * q^86 + 32 * q^89 - 8 * q^91 + 24 * q^94 + 4 * q^96 - 8 * q^99

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.b.a	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		✓			1850.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+3 i q^{3}-q^{4}-3 q^{6}-i q^{8}+\cdots\)
1850.2.b.b	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None					370.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}+2 i q^{7}+\cdots\)
1850.2.b.c	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None					370.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+2 i q^{3}-q^{4}-2 q^{6}-i q^{7}+\cdots\)
1850.2.b.d	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None					370.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{4}+i q^{8}+3 q^{9}-4 q^{11}+\cdots\)
1850.2.b.e	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		✓			1850.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+i q^{3}-q^{4}+q^{6}+4 i q^{7}+\cdots\)
1850.2.b.f	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		✓			1850.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+2 i q^{3}-q^{4}+2 q^{6}-4 i q^{7}+\cdots\)
1850.2.b.g	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None					370.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+2 i q^{3}-q^{4}+2 q^{6}-i q^{7}+\cdots\)
1850.2.b.h	$1850$	$2$	1850.b	5.b	$2$	$2$	$2$	$14.772$	\(\Q(\sqrt{-1}) \)	None		✓			1850.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+2 i q^{3}-q^{4}+2 q^{6}+i q^{8}+\cdots\)
1850.2.b.i	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	\(\Q(i, \sqrt{13})\)	None					74.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}-q^{4}+(-2+\cdots)q^{6}+\cdots\)
1850.2.b.j	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	\(\Q(i, \sqrt{5})\)	None					74.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{2}q^{6}-2\beta _{1}q^{7}+\cdots\)
1850.2.b.k	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	\(\Q(i, \sqrt{6})\)	None		✓			1850.2.a.r	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}-q^{4}+(1+\beta _{3})q^{6}+\cdots\)
1850.2.b.l	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	\(\Q(\zeta_{12})\)	None					370.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{2}+(-\beta_{2}+\beta_1)q^{3}-q^{4}+\cdots\)
1850.2.b.m	$1850$	$2$	1850.b	5.b	$2$	$4$	$4$	$14.772$	\(\Q(i, \sqrt{33})\)	None					370.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+2\beta _{2}q^{3}-q^{4}+2q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1850.2.b.n	$1850$	$2$	1850.b	5.b	$2$	$6$	$6$	$14.772$	6.0.350464.1	None		✓			1850.2.a.ba	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(\beta _{3}-\beta _{5})q^{3}-q^{4}+(-1+\cdots)q^{6}+\cdots\)
1850.2.b.o	$1850$	$2$	1850.b	5.b	$2$	$6$	$6$	$14.772$	6.0.3182656.1	None					370.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{2}q^{6}-\beta _{5}q^{7}+\cdots\)
1850.2.b.p	$1850$	$2$	1850.b	5.b	$2$	$6$	$6$	$14.772$	6.0.37161216.1	None		✓			1850.2.a.y	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{2}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1850, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(925, [\chi])\)\(^{\oplus 2}\)