Space of modular forms of level 50, weight 18, and Character 50.b

• Label: 50.18.b
• Level: $50$
• Weight: $18$
• Character orbit: 50.b
• Rep. character: $\chi_{50}(49,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $7$
• Sturm bound: $135$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(135\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(50, [\chi])\).

	Total	New	Old
Modular forms	134	26	108
Cusp forms	122	26	96
Eisenstein series	12	0	12

Trace form

26 * q - 1703936 * q^4 - 1409536 * q^6 - 1153480348 * q^9 - 240451878 * q^11 - 22617832448 * q^14 + 111669149696 * q^16 + 175209015830 * q^19 - 25960786348 * q^21 + 92375351296 * q^24 + 1238593931264 * q^26 - 9576723310080 * q^29 + 16777758849412 * q^31 + 13272942377472 * q^34 + 75594488086528 * q^36 + 68445826492264 * q^39 + 367976953283682 * q^41 + 15758254276608 * q^44 + 182559006372864 * q^46 - 1026492082035282 * q^49 + 2480434404138522 * q^51 - 1933642837936640 * q^54 + 1482282267312128 * q^56 - 1525048304962560 * q^59 + 4209990299013172 * q^61 - 7318349394477056 * q^64 + 5793658873579008 * q^66 - 37469833807025436 * q^69 + 7378802909585592 * q^71 + 13500741124621312 * q^74 - 11482498061434880 * q^76 + 39147002887312820 * q^79 + 90375099044809786 * q^81 + 1701366094102528 * q^84 + 48955877574232064 * q^86 + 152441441689654410 * q^89 - 233017027674676048 * q^91 - 39604703781562368 * q^94 - 6053911022534656 * q^96 + 392591346264814644 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(50, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
50.18.b.a	$50$	$18$	50.b	5.b	$2$	$2$	$2$	$91.611$	\(\Q(\sqrt{-1}) \)	None					10.18.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+128\beta q^{2}+7488\beta q^{3}-65536 q^{4}+\cdots\)
50.18.b.b	$50$	$18$	50.b	5.b	$2$	$2$	$2$	$91.611$	\(\Q(\sqrt{-1}) \)	None					2.18.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-128\beta q^{2}+3042\beta q^{3}-65536 q^{4}+\cdots\)
50.18.b.c	$50$	$18$	50.b	5.b	$2$	$4$	$4$	$91.611$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		✓			50.18.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{8}\beta _{1}q^{2}+(-5796\beta _{1}-\beta _{2})q^{3}+\cdots\)
50.18.b.d	$50$	$18$	50.b	5.b	$2$	$4$	$4$	$91.611$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None					10.18.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2^{7}\beta _{1}q^{2}+(-327\beta _{1}+\beta _{2})q^{3}-2^{16}q^{4}+\cdots\)
50.18.b.e	$50$	$18$	50.b	5.b	$2$	$4$	$4$	$91.611$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None					10.18.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{7}\beta _{1}q^{2}+(1577\beta _{1}-\beta _{2})q^{3}-2^{16}q^{4}+\cdots\)
50.18.b.f	$50$	$18$	50.b	5.b	$2$	$4$	$4$	$91.611$	\(\Q(i, \sqrt{2941})\)	None					10.18.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{7}\beta _{1}q^{2}+(4407\beta _{1}+\beta _{2})q^{3}-2^{16}q^{4}+\cdots\)
50.18.b.g	$50$	$18$	50.b	5.b	$2$	$6$	$6$	$91.611$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		✓	✓		50.18.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2^{8}\beta _{1}q^{2}+(-2504\beta _{1}-\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(50, [\chi])\) into lower level spaces

\( S_{18}^{\mathrm{old}}(50, [\chi]) \simeq \) \(S_{18}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)