Space of modular forms of level 95, weight 11, and Character 95.j

• Label: 95.11.j
• Level: $95$
• Weight: $11$
• Character orbit: 95.j
• Rep. character: $\chi_{95}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $136$
• Newform subspaces: $1$
• Sturm bound: $110$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(110\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(95, [\chi])\).

	Total	New	Old
Modular forms	204	136	68
Cusp forms	196	136	60
Eisenstein series	8	0	8

Trace form

136 * q - 132 * q^3 + 37474 * q^4 - 1022 * q^6 - 76620 * q^7 + 1448988 * q^9 + 93750 * q^10 + 418144 * q^11 - 1256574 * q^13 + 612480 * q^14 - 20575630 * q^16 + 3635834 * q^17 + 10572814 * q^19 + 8494308 * q^21 - 31311360 * q^22 - 11728554 * q^23 - 1627348 * q^24 - 132812500 * q^25 - 5280948 * q^26 - 81401852 * q^28 - 36928518 * q^29 + 79750000 * q^30 + 196574250 * q^32 + 359004150 * q^33 + 205341462 * q^34 + 19937500 * q^35 - 1128154804 * q^36 + 1584974 * q^38 + 224945180 * q^39 + 96000000 * q^40 + 1170402744 * q^41 + 173440898 * q^42 - 390292220 * q^43 - 49120052 * q^44 - 148625000 * q^45 - 445097680 * q^47 + 362033562 * q^48 + 3958185060 * q^49 + 995976516 * q^51 + 7766334 * q^52 + 815693040 * q^53 + 2049344062 * q^54 + 3831676392 * q^57 + 3983452220 * q^58 + 2842939668 * q^59 - 1389656250 * q^60 + 1929307508 * q^61 - 2885441744 * q^62 - 5022307122 * q^63 - 29425336368 * q^64 + 2939512012 * q^66 + 1891858296 * q^67 + 18554561860 * q^68 - 810562500 * q^70 - 8973340848 * q^71 + 7541812308 * q^72 + 4947578188 * q^73 - 23389998076 * q^74 + 15724739728 * q^76 - 5682818404 * q^77 - 10507817400 * q^78 + 16066927146 * q^79 + 3604750000 * q^80 - 43776877608 * q^81 - 13564413998 * q^82 + 2628386824 * q^83 - 2399750000 * q^85 + 38885030448 * q^86 + 12840668220 * q^87 - 35640122064 * q^89 + 3198281250 * q^90 + 4174912572 * q^91 - 23134882520 * q^92 - 36221884016 * q^93 - 1613500000 * q^95 + 13864395128 * q^96 - 23558943450 * q^97 + 31730410686 * q^98 - 8878413234 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(95, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
95.11.j.a	$95$	$11$	95.j	19.d	$6$	$136$	$68$	$60.359$		None		✓	✓	✓	95.11.j.a	$2$	$0$	\(0\)	\(-132\)	\(0\)	\(-76620\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{11}^{\mathrm{old}}(95, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(95, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)