Space of modular forms of level 35, weight 4, and Character 35.e

• Label: 35.4.e
• Level: $35$
• Weight: $4$
• Character orbit: 35.e
• Rep. character: $\chi_{35}(11,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $16$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	35.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(16\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(35, [\chi])\).

	Total	New	Old
Modular forms	28	16	12
Cusp forms	20	16	4
Eisenstein series	8	0	8

Trace form

16 * q + 2 * q^2 + 12 * q^3 - 42 * q^4 + 10 * q^5 + 8 * q^6 - 68 * q^7 + 36 * q^8 - 42 * q^9 + 20 * q^10 - 30 * q^11 + 34 * q^12 + 48 * q^13 + 70 * q^14 + 40 * q^15 - 86 * q^16 + 132 * q^17 + 48 * q^18 - 18 * q^19 - 280 * q^20 + 242 * q^21 + 688 * q^22 - 248 * q^23 - 728 * q^24 - 200 * q^25 - 278 * q^26 - 840 * q^27 + 770 * q^28 - 444 * q^29 + 140 * q^30 - 168 * q^31 + 98 * q^32 + 320 * q^33 + 824 * q^34 - 110 * q^35 + 2028 * q^36 + 820 * q^37 - 96 * q^38 + 188 * q^39 + 240 * q^40 - 384 * q^41 - 2970 * q^42 - 768 * q^43 - 890 * q^44 + 600 * q^45 - 142 * q^46 + 624 * q^47 + 164 * q^48 + 866 * q^49 - 100 * q^50 - 268 * q^51 + 668 * q^52 + 4 * q^53 + 72 * q^54 - 640 * q^55 - 1464 * q^56 + 1448 * q^57 - 1842 * q^58 - 1188 * q^59 - 810 * q^60 - 2434 * q^61 + 360 * q^62 + 2660 * q^63 - 588 * q^64 - 110 * q^65 - 1988 * q^66 + 448 * q^67 + 4696 * q^68 + 3324 * q^69 + 1600 * q^70 + 3952 * q^71 + 1472 * q^72 + 1156 * q^73 + 2270 * q^74 + 300 * q^75 + 852 * q^76 - 1512 * q^77 - 11000 * q^78 + 240 * q^79 + 1280 * q^80 + 788 * q^81 - 2050 * q^82 - 5280 * q^83 - 876 * q^84 - 1280 * q^85 + 3104 * q^86 - 1684 * q^87 - 3680 * q^88 - 1778 * q^89 + 540 * q^90 - 2124 * q^91 - 292 * q^92 + 780 * q^93 + 2210 * q^94 - 300 * q^95 - 6404 * q^96 + 1744 * q^97 + 7654 * q^98 + 2172 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(35, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.4.e.a	$35$	$4$	35.e	7.c	$3$	$2$	$1$	$2.065$	\(\Q(\sqrt{-3}) \)	None		✓			35.4.e.a	$2$	$0$	\(-3\)	\(2\)	\(-5\)	\(-28\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-3\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
35.4.e.b	$35$	$4$	35.e	7.c	$3$	$4$	$2$	$2.065$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			35.4.e.b	$2$	$0$	\(6\)	\(2\)	\(-10\)	\(22\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-3\beta _{2}+\beta _{3})q^{2}+(1+3\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
35.4.e.c	$35$	$4$	35.e	7.c	$3$	$10$	$5$	$2.065$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓	✓		35.4.e.c	$2$	$0$	\(-1\)	\(8\)	\(25\)	\(-62\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+(-\beta _{3}-\beta _{5}+2\beta _{6}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(35, [\chi])\) into lower level spaces

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