Space of modular forms of level 245, weight 4, and Character 245.e

• Label: 245.4.e
• Level: $245$
• Weight: $4$
• Character orbit: 245.e
• Rep. character: $\chi_{245}(116,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $80$
• Newform subspaces: $17$
• Sturm bound: $112$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(112\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(245, [\chi])\).

	Total	New	Old
Modular forms	184	80	104
Cusp forms	152	80	72
Eisenstein series	32	0	32

Trace form

80 * q - 4 * q^2 - 12 * q^3 - 140 * q^4 - 10 * q^5 - 8 * q^6 - 72 * q^8 - 406 * q^9 - 20 * q^10 + 46 * q^11 - 34 * q^12 - 48 * q^13 - 80 * q^15 - 752 * q^16 - 132 * q^17 - 138 * q^18 + 18 * q^19 + 280 * q^20 - 984 * q^22 + 412 * q^23 + 728 * q^24 - 1000 * q^25 + 278 * q^26 + 840 * q^27 + 636 * q^29 - 140 * q^30 + 168 * q^31 + 224 * q^32 - 320 * q^33 - 824 * q^34 + 1040 * q^36 + 180 * q^37 + 96 * q^38 + 632 * q^39 - 240 * q^40 + 384 * q^41 - 424 * q^43 + 1150 * q^44 - 600 * q^45 + 578 * q^46 - 624 * q^47 - 164 * q^48 + 200 * q^50 + 88 * q^51 - 668 * q^52 + 20 * q^53 - 72 * q^54 + 640 * q^55 + 408 * q^57 + 3334 * q^58 + 1188 * q^59 + 1130 * q^60 + 2434 * q^61 - 360 * q^62 + 7784 * q^64 + 430 * q^65 + 1988 * q^66 - 2716 * q^67 - 4696 * q^68 - 3324 * q^69 - 6224 * q^71 - 2650 * q^72 - 1156 * q^73 - 3798 * q^74 - 300 * q^75 - 852 * q^76 + 15280 * q^78 - 3700 * q^79 - 1280 * q^80 - 5412 * q^81 + 2050 * q^82 + 5280 * q^83 + 2000 * q^85 + 3144 * q^86 + 1684 * q^87 + 13352 * q^88 + 1778 * q^89 - 540 * q^90 - 13780 * q^92 - 4332 * q^93 - 2210 * q^94 + 320 * q^95 + 6404 * q^96 - 1744 * q^97 - 22516 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(245, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
245.4.e.a	$245$	$4$	245.e	7.c	$3$	$2$	$1$	$14.455$	\(\Q(\sqrt{-3}) \)	None					35.4.e.a	$2$	$1$	\(-3\)	\(-2\)	\(5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
245.4.e.b	$245$	$4$	245.e	7.c	$3$	$2$	$1$	$14.455$	\(\Q(\sqrt{-3}) \)	None					35.4.a.a	$2$	$0$	\(-1\)	\(-8\)	\(-5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-8+8\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
245.4.e.c	$245$	$4$	245.e	7.c	$3$	$2$	$1$	$14.455$	\(\Q(\sqrt{-3}) \)	None		✓			245.4.a.b	$2$	$0$	\(-1\)	\(-6\)	\(5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-6+6\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
245.4.e.d	$245$	$4$	245.e	7.c	$3$	$2$	$1$	$14.455$	\(\Q(\sqrt{-3}) \)	None		✓			245.4.a.b	$2$	$0$	\(-1\)	\(6\)	\(-5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(6-6\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
245.4.e.e	$245$	$4$	245.e	7.c	$3$	$2$	$1$	$14.455$	\(\Q(\sqrt{-3}) \)	None					35.4.a.a	$2$	$0$	\(-1\)	\(8\)	\(5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(8-8\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
245.4.e.f	$245$	$4$	245.e	7.c	$3$	$2$	$1$	$14.455$	\(\Q(\sqrt{-3}) \)	None					5.4.a.a	$2$	$0$	\(4\)	\(-2\)	\(5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
245.4.e.g	$245$	$4$	245.e	7.c	$3$	$2$	$1$	$14.455$	\(\Q(\sqrt{-3}) \)	None					5.4.a.a	$2$	$0$	\(4\)	\(2\)	\(-5\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+4\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
245.4.e.h	$245$	$4$	245.e	7.c	$3$	$4$	$2$	$14.455$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					35.4.a.b	$2$	$0$	\(-8\)	\(-2\)	\(10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+4\beta _{2}-\beta _{3})q^{2}+(-1-4\beta _{1}+\cdots)q^{3}+\cdots\)
245.4.e.i	$245$	$4$	245.e	7.c	$3$	$4$	$2$	$14.455$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					35.4.a.b	$2$	$0$	\(-8\)	\(2\)	\(-10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+4\beta _{2}-\beta _{3})q^{2}+(1+4\beta _{1}+\cdots)q^{3}+\cdots\)
245.4.e.j	$245$	$4$	245.e	7.c	$3$	$4$	$2$	$14.455$	\(\Q(\sqrt{-3}, \sqrt{11})\)	None		✓			245.4.a.i	$2$	$0$	\(-2\)	\(-10\)	\(-10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}-\beta _{2})q^{2}+5\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
245.4.e.k	$245$	$4$	245.e	7.c	$3$	$4$	$2$	$14.455$	\(\Q(\sqrt{-3}, \sqrt{11})\)	None		✓			245.4.a.i	$2$	$0$	\(-2\)	\(10\)	\(10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}-\beta _{2})q^{2}-5\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
245.4.e.l	$245$	$4$	245.e	7.c	$3$	$4$	$2$	$14.455$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None					35.4.e.b	$2$	$0$	\(6\)	\(-2\)	\(10\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-3\beta _{2}+\beta _{3})q^{2}+(-1-3\beta _{1}+\cdots)q^{3}+\cdots\)
245.4.e.m	$245$	$4$	245.e	7.c	$3$	$6$	$3$	$14.455$	6.0.5567659200.1	None					35.4.a.c	$2$	$0$	\(3\)	\(-2\)	\(-15\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1}-\beta _{2}-\beta _{3})q^{2}+(\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
245.4.e.n	$245$	$4$	245.e	7.c	$3$	$6$	$3$	$14.455$	6.0.5567659200.1	None					35.4.a.c	$2$	$0$	\(3\)	\(2\)	\(15\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1}-\beta _{2}-\beta _{3})q^{2}+(-\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
245.4.e.o	$245$	$4$	245.e	7.c	$3$	$10$	$5$	$14.455$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None					35.4.e.c	$2$	$0$	\(-1\)	\(-8\)	\(-25\)	\(0\)	$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+(-\beta _{3}-\beta _{5}-2\beta _{7}+\cdots)q^{3}+\cdots\)
245.4.e.p	$245$	$4$	245.e	7.c	$3$	$12$	$6$	$14.455$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			245.4.a.o	$2$	$0$	\(2\)	\(-16\)	\(30\)	\(0\)	$2^{2}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{2}+(-3-3\beta _{3}+\beta _{7}+\beta _{9})q^{3}+\cdots\)
245.4.e.q	$245$	$4$	245.e	7.c	$3$	$12$	$6$	$14.455$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓			245.4.a.o	$2$	$0$	\(2\)	\(16\)	\(-30\)	\(0\)	$2^{2}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{2}+(3+3\beta _{3}-\beta _{7}-\beta _{9})q^{3}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(245, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)