Space of modular forms of level 90, weight 11, and Character 90.h

• Label: 90.11.h
• Level: $90$
• Weight: $11$
• Character orbit: 90.h
• Rep. character: $\chi_{90}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $1$
• Sturm bound: $198$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	90.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(198\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(90, [\chi])\).

	Total	New	Old
Modular forms	368	80	288
Cusp forms	352	80	272
Eisenstein series	16	0	16

Trace form

80 * q + 44 * q^3 + 20480 * q^4 - 13568 * q^6 - 24476 * q^7 - 103396 * q^9 + 1944 * q^11 + 45056 * q^12 + 561100 * q^13 - 175680 * q^14 - 687500 * q^15 - 10485760 * q^16 - 3888896 * q^18 + 5932480 * q^19 + 30706612 * q^21 - 6946944 * q^22 - 2008908 * q^23 - 2392064 * q^24 + 78125000 * q^25 - 33902836 * q^27 - 25063424 * q^28 - 54816192 * q^29 - 19000000 * q^30 + 11191216 * q^31 - 38758416 * q^33 - 61492992 * q^34 - 176128 * q^36 + 204029848 * q^37 - 247344768 * q^38 - 27399560 * q^39 + 306039276 * q^41 + 146895872 * q^42 + 173186188 * q^43 + 8500000 * q^45 + 366913920 * q^46 - 1316963016 * q^47 + 11534336 * q^48 - 1286128428 * q^49 + 1792903968 * q^51 - 287283200 * q^52 - 1612000448 * q^54 - 89948160 * q^56 - 2228035028 * q^57 + 5720414040 * q^59 + 352000000 * q^60 - 1218762932 * q^61 - 6364657976 * q^63 - 10737418240 * q^64 - 2716312500 * q^65 - 6187488768 * q^66 + 1597633744 * q^67 + 1475831808 * q^68 + 18144078528 * q^69 + 183000000 * q^70 + 948699136 * q^72 - 10426752656 * q^73 - 15538503168 * q^74 - 85937500 * q^75 + 1518714880 * q^76 + 18397247724 * q^77 + 14163069824 * q^78 + 3046073392 * q^79 - 16327365376 * q^81 + 10345792512 * q^82 - 27645650316 * q^83 - 372180992 * q^84 - 2312062500 * q^85 + 6643133568 * q^86 - 5895407700 * q^87 + 3556835328 * q^88 + 7832000000 * q^90 + 11114363408 * q^91 - 1028560896 * q^92 + 4525684516 * q^93 - 6416128320 * q^94 - 17922375000 * q^95 + 2332033024 * q^96 - 10980388424 * q^97 - 78067269744 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(90, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
90.11.h.a	$90$	$11$	90.h	9.d	$6$	$80$	$40$	$57.182$		None		✓	✓	✓	90.11.h.a	$2$	$0$	\(0\)	\(44\)	\(0\)	\(-24476\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{11}^{\mathrm{old}}(90, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(90, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)