Space of modular forms of level 35, weight 10, and Character 35.e

• Label: 35.10.e
• Level: $35$
• Weight: $10$
• Character orbit: 35.e
• Rep. character: $\chi_{35}(11,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $40$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	35.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(40\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(35, [\chi])\).

	Total	New	Old
Modular forms	76	48	28
Cusp forms	68	48	20
Eisenstein series	8	0	8

Trace form

48 * q + 34 * q^2 - 324 * q^3 - 6314 * q^4 - 1250 * q^5 + 4544 * q^6 - 3876 * q^7 - 67932 * q^8 - 141414 * q^9 - 20000 * q^10 - 78910 * q^11 - 193502 * q^12 + 639344 * q^13 + 424970 * q^14 + 265000 * q^15 - 2211558 * q^16 - 726916 * q^17 + 1712064 * q^18 + 500174 * q^19 + 1015000 * q^20 + 4090286 * q^21 - 2002624 * q^22 + 33416 * q^23 - 11734856 * q^24 - 9375000 * q^25 + 1855086 * q^26 + 18415320 * q^27 + 9775010 * q^28 - 16103908 * q^29 - 2380000 * q^30 - 9552424 * q^31 - 3892014 * q^32 - 15576640 * q^33 + 71723608 * q^34 + 7591250 * q^35 + 18266844 * q^36 - 52316660 * q^37 - 92967488 * q^38 + 58836236 * q^39 - 15360000 * q^40 - 25959632 * q^41 + 200452110 * q^42 - 209180224 * q^43 - 143171010 * q^44 - 14250000 * q^45 + 130857994 * q^46 - 120782752 * q^47 + 513498212 * q^48 + 87674942 * q^49 - 26562500 * q^50 - 148529884 * q^51 - 217058244 * q^52 - 143397508 * q^53 - 60156 * q^54 + 224080000 * q^55 - 373221192 * q^56 + 42487736 * q^57 + 137976654 * q^58 + 46816604 * q^59 - 324146250 * q^60 + 345410298 * q^61 - 118990680 * q^62 - 369615820 * q^63 + 1603477204 * q^64 + 154933750 * q^65 + 1232991676 * q^66 - 62059424 * q^67 - 545621672 * q^68 - 2753035692 * q^69 - 241787500 * q^70 + 1550828816 * q^71 + 1424976944 * q^72 + 751678348 * q^73 + 201936930 * q^74 - 126562500 * q^75 - 2859908284 * q^76 - 2264436104 * q^77 + 874863400 * q^78 + 459477920 * q^79 - 341760000 * q^80 - 1208887276 * q^81 - 322489250 * q^82 - 1277519840 * q^83 + 2354148 * q^84 - 279520000 * q^85 + 315232332 * q^86 - 1348411348 * q^87 + 474317360 * q^88 - 355814886 * q^89 + 3117802500 * q^90 + 203935988 * q^91 - 2218184004 * q^92 - 201286860 * q^93 + 1801884670 * q^94 - 284437500 * q^95 + 1214975308 * q^96 + 8287090288 * q^97 + 4046160982 * q^98 + 8874667164 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(35, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.10.e.a	$35$	$10$	35.e	7.c	$3$	$22$	$11$	$18.026$		None		✓			35.10.e.a	$2$	$0$	\(33\)	\(-56\)	\(6875\)	\(4586\)		$\mathrm{SU}(2)[C_{3}]$
35.10.e.b	$35$	$10$	35.e	7.c	$3$	$26$	$13$	$18.026$		None		✓	✓		35.10.e.b	$2$	$0$	\(1\)	\(-268\)	\(-8125\)	\(-8462\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{10}^{\mathrm{old}}(35, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(35, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)