Space of modular forms of level 245, weight 6, and Character 245.b

• Label: 245.6.b
• Level: $245$
• Weight: $6$
• Character orbit: 245.b
• Rep. character: $\chi_{245}(99,\cdot)$
• Character field: $\Q$
• Dimension: $98$
• Newform subspaces: $7$
• Sturm bound: $168$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	245.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(168\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(245, [\chi])\).

	Total	New	Old
Modular forms	148	108	40
Cusp forms	132	98	34
Eisenstein series	16	10	6

Trace form

98 * q - 1492 * q^4 - 66 * q^5 - 84 * q^6 - 7270 * q^9 - 464 * q^10 + 464 * q^11 + 1032 * q^15 + 18092 * q^16 + 1592 * q^19 + 2492 * q^20 + 19032 * q^24 - 2694 * q^25 - 13492 * q^26 - 12040 * q^29 + 3116 * q^30 - 20052 * q^31 - 1972 * q^34 + 132156 * q^36 - 19504 * q^39 + 53340 * q^40 + 7440 * q^41 - 59388 * q^44 + 36438 * q^45 + 77068 * q^46 - 5924 * q^50 + 21408 * q^51 + 4404 * q^54 - 14212 * q^55 - 63396 * q^59 - 221792 * q^60 - 167388 * q^61 - 118012 * q^64 - 99044 * q^65 + 182308 * q^66 + 121084 * q^69 - 117832 * q^71 + 254732 * q^74 + 140232 * q^75 - 139888 * q^76 - 194816 * q^79 - 280356 * q^80 + 806698 * q^81 + 13536 * q^85 + 416176 * q^86 + 161308 * q^89 + 25172 * q^90 + 241556 * q^94 - 205952 * q^95 - 859632 * q^96 - 62184 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(245, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
245.6.b.a	$245$	$6$	245.b	5.b	$2$	$2$	$2$	$39.294$	\(\Q(\sqrt{-11}) \)	None					5.6.b.a	$2$	$0$	\(0\)	\(0\)	\(90\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{2}-3\beta q^{3}-12q^{4}+(45+5\beta )q^{5}+\cdots\)
245.6.b.b	$245$	$6$	245.b	5.b	$2$	$2$	$2$	$39.294$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-35}) \)		✓			245.6.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{3}+2^{5}q^{4}-5\beta q^{5}+118q^{9}+\cdots\)
245.6.b.c	$245$	$6$	245.b	5.b	$2$	$12$	$12$	$39.294$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			245.6.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 5^{3}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-\beta _{4}q^{3}+(-20+\beta _{1})q^{4}+\cdots\)
245.6.b.d	$245$	$6$	245.b	5.b	$2$	$14$	$14$	$39.294$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None					35.6.b.a	$2$	$0$	\(0\)	\(0\)	\(-156\)	\(0\)	$2^{4}\cdot 5^{3}\cdot 7^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-\beta _{6}q^{3}+(-15+\beta _{1})q^{4}+\cdots\)
245.6.b.e	$245$	$6$	245.b	5.b	$2$	$18$	$18$	$39.294$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None					35.6.j.a	$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{18}\cdot 5^{7}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-14+\beta _{2})q^{4}+\cdots\)
245.6.b.f	$245$	$6$	245.b	5.b	$2$	$18$	$18$	$39.294$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None					35.6.j.a	$2$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{18}\cdot 5^{7}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-14+\beta _{2})q^{4}+\cdots\)
245.6.b.g	$245$	$6$	245.b	5.b	$2$	$32$	$32$	$39.294$		None		✓	✓		245.6.b.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(245, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)