Space of modular forms of level 245, weight 2, and Character 245.j

• Label: 245.2.j
• Level: $245$
• Weight: $2$
• Character orbit: 245.j
• Rep. character: $\chi_{245}(79,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $7$
• Sturm bound: $56$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(56\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(3\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(245, [\chi])\).

	Total	New	Old
Modular forms	72	48	24
Cusp forms	40	32	8
Eisenstein series	32	16	16

Trace form

32 * q + 14 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^9 + 4 * q^10 - 2 * q^11 - 28 * q^15 - 2 * q^16 - 12 * q^19 - 4 * q^20 - 6 * q^24 - 8 * q^25 + 4 * q^26 + 8 * q^29 - 30 * q^30 + 4 * q^31 + 8 * q^34 - 80 * q^36 + 6 * q^39 + 12 * q^40 - 20 * q^41 + 68 * q^44 + 4 * q^45 - 34 * q^46 + 24 * q^50 - 50 * q^51 - 10 * q^54 - 20 * q^59 - 48 * q^60 + 14 * q^61 + 76 * q^64 - 42 * q^65 + 12 * q^69 - 8 * q^71 + 48 * q^74 + 8 * q^75 + 24 * q^76 + 10 * q^79 - 2 * q^80 + 48 * q^81 + 4 * q^85 + 18 * q^86 - 18 * q^89 - 16 * q^90 + 20 * q^95 - 10 * q^96 - 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(245, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
245.2.j.a	$245$	$2$	245.j	35.j	$6$	$4$	$2$	$1.956$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			245.2.b.e	$4$	$0$	\(0\)	\(-6\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+(4+4\beta _{2}+\cdots)q^{4}+\cdots\)
245.2.j.b	$245$	$2$	245.j	35.j	$6$	$4$	$2$	$1.956$	\(\Q(\sqrt{-3}, \sqrt{-5})\)	\(\Q(\sqrt{-35}) \)		✓			245.2.b.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{1}q^{3}+(-2+2\beta _{2})q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
245.2.j.c	$245$	$2$	245.j	35.j	$6$	$4$	$2$	$1.956$	\(\Q(\zeta_{12})\)	None					35.2.j.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
245.2.j.d	$245$	$2$	245.j	35.j	$6$	$4$	$2$	$1.956$	\(\Q(\zeta_{12})\)	None					35.2.b.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
245.2.j.e	$245$	$2$	245.j	35.j	$6$	$4$	$2$	$1.956$	\(\Q(\zeta_{12})\)	None					35.2.b.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
245.2.j.f	$245$	$2$	245.j	35.j	$6$	$4$	$2$	$1.956$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			245.2.b.e	$4$	$0$	\(0\)	\(6\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(4+4\beta _{2}+\cdots)q^{4}+\cdots\)
245.2.j.g	$245$	$2$	245.j	35.j	$6$	$8$	$4$	$1.956$	\(\Q(\zeta_{24})\)	None		✓	✓		245.2.b.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{2}+(2\zeta_{24}^{3}+2\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

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