Space of modular forms of level 59, weight 7, and Character 59.d

• Label: 59.7.d
• Level: $59$
• Weight: $7$
• Character orbit: 59.d
• Rep. character: $\chi_{59}(2,\cdot)$
• Character field: $\Q(\zeta_{58})$
• Dimension: $812$
• Newform subspaces: $1$
• Sturm bound: $35$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 59 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	59.d (of order \(58\) and degree \(28\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 59 \)
Character field:			\(\Q(\zeta_{58})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(35\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(59, [\chi])\).

	Total	New	Old
Modular forms	868	868	0
Cusp forms	812	812	0
Eisenstein series	56	56	0

Trace form

812 * q - 29 * q^2 - 39 * q^3 + 869 * q^4 - 171 * q^5 - 29 * q^6 - 435 * q^7 - 29 * q^8 - 7648 * q^9 - 29 * q^10 - 29 * q^11 + 1095 * q^12 - 29 * q^13 - 29 * q^14 - 569 * q^15 - 25051 * q^16 - 9071 * q^17 - 29 * q^18 - 3879 * q^19 + 46867 * q^20 - 3729 * q^21 - 11267 * q^22 - 29 * q^23 - 29 * q^24 - 65696 * q^25 + 64561 * q^26 - 36009 * q^27 + 45513 * q^28 + 31701 * q^29 - 29 * q^30 - 29 * q^31 - 29 * q^32 - 29 * q^33 - 29 * q^34 - 46305 * q^35 + 185269 * q^36 - 29 * q^37 - 29 * q^38 - 29 * q^39 - 29 * q^40 - 91943 * q^41 - 29 * q^42 - 29 * q^43 - 29 * q^44 + 1328609 * q^45 + 122071 * q^46 - 472149 * q^47 - 4460721 * q^48 - 992540 * q^49 - 1117341 * q^50 - 161065 * q^51 + 1336291 * q^52 + 1079813 * q^53 + 4504947 * q^54 + 1872907 * q^55 + 3956963 * q^56 + 2677007 * q^57 - 302138 * q^59 - 4965482 * q^60 - 1574381 * q^61 - 2444409 * q^62 - 5085047 * q^63 - 5066455 * q^64 - 1422653 * q^65 + 433939 * q^66 + 876931 * q^67 + 3018437 * q^68 + 5706243 * q^69 + 6798499 * q^70 + 3537645 * q^71 + 6041251 * q^72 - 396749 * q^73 - 3448403 * q^74 - 9552475 * q^75 - 247173 * q^76 - 29 * q^77 + 375035 * q^78 - 4731 * q^79 - 1921013 * q^80 + 841594 * q^81 - 29 * q^82 - 29 * q^83 - 2367333 * q^84 - 864073 * q^85 - 5031139 * q^86 + 4790463 * q^87 - 726023 * q^88 - 29 * q^89 - 29 * q^90 - 29 * q^91 - 29 * q^92 - 29 * q^93 - 2835797 * q^94 - 1047881 * q^95 - 29 * q^96 - 29 * q^97 + 29127484 * q^98 + 9513421 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(59, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
59.7.d.a	$59$	$7$	59.d	59.d	$58$	$812$	$29$	$13.573$		None		✓	✓	✓	59.7.d.a	$2$	$0$	\(-29\)	\(-39\)	\(-171\)	\(-435\)		$\mathrm{SU}(2)[C_{58}]$