## Results (48 matches)

Label Dim $A$ Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
83.1.b.a $1$ $0.041$ $$\Q$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$-1$$ $$0$$ $$-1$$ $$q-q^{3}+q^{4}-q^{7}-q^{11}-q^{12}+q^{16}+\cdots$$
83.2.a.a $1$ $0.663$ $$\Q$$ None None $$-1$$ $$-1$$ $$-2$$ $$-3$$ $+$ $$q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}-3q^{7}+\cdots$$
83.2.a.b $6$ $0.663$ 6.6.9059636.1 None None $$1$$ $$1$$ $$2$$ $$3$$ $-$ $$q+(-\beta _{1}-\beta _{2})q^{2}-\beta _{3}q^{3}+(1-\beta _{5})q^{4}+\cdots$$
83.2.c.a $240$ $0.663$ None None $$-38$$ $$-37$$ $$-35$$ $$-33$$
83.3.b.a $3$ $2.262$ 3.3.2241.1 $$\Q(\sqrt{-83})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{2})q^{3}+4q^{4}+(-3\beta _{1}-2\beta _{2})q^{7}+\cdots$$
83.3.b.b $10$ $2.262$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None None $$0$$ $$-6$$ $$0$$ $$12$$ $$q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+(-3+\beta _{7}+\cdots)q^{4}+\cdots$$
83.3.d.a $520$ $2.262$ None None $$-41$$ $$-35$$ $$-41$$ $$-53$$
83.4.a.a $7$ $4.897$ $$\mathbb{Q}[x]/(x^{7} - \cdots)$$ None None $$-5$$ $$-11$$ $$-17$$ $$-46$$ $-$ $$q+(-1-\beta _{4})q^{2}+(-1+\beta _{1}+\beta _{4})q^{3}+\cdots$$
83.4.a.b $13$ $4.897$ $$\mathbb{Q}[x]/(x^{13} - \cdots)$$ None None $$5$$ $$7$$ $$33$$ $$52$$ $+$ $$q+\beta _{1}q^{2}+(1+\beta _{8})q^{3}+(6+\beta _{2})q^{4}+\cdots$$
83.4.c.a $800$ $4.897$ None None $$-41$$ $$-37$$ $$-57$$ $$-47$$
83.5.b.a $3$ $8.580$ 3.3.2241.1 $$\Q(\sqrt{-83})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(2\beta _{1}-3\beta _{2})q^{3}+2^{4}q^{4}+(21\beta _{1}-11\beta _{2})q^{7}+\cdots$$
83.5.b.b $24$ $8.580$ None None $$0$$ $$6$$ $$0$$ $$-112$$
83.5.d.a $1080$ $8.580$ None None $$-41$$ $$-47$$ $$-41$$ $$71$$
83.6.a.a $14$ $13.312$ $$\mathbb{Q}[x]/(x^{14} - \cdots)$$ None None $$-13$$ $$-17$$ $$-162$$ $$-247$$ $+$ $$q+(-1+\beta _{1})q^{2}+(-1+\beta _{7})q^{3}+(10+\cdots)q^{4}+\cdots$$
83.6.a.b $20$ $13.312$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None None $$7$$ $$37$$ $$88$$ $$439$$ $-$ $$q+\beta _{1}q^{2}+(2+\beta _{5})q^{3}+(19+\beta _{2})q^{4}+\cdots$$
83.6.c.a $1360$ $13.312$ None None $$-35$$ $$-61$$ $$33$$ $$-233$$
83.7.b.a $1$ $19.094$ $$\Q$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$-29$$ $$0$$ $$-61$$ $$q-29q^{3}+2^{6}q^{4}-61q^{7}+112q^{9}+\cdots$$
83.7.b.b $2$ $19.094$ $$\Q(\sqrt{249})$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$29$$ $$0$$ $$61$$ $$q+(15+\beta )q^{3}+2^{6}q^{4}+(23-15\beta )q^{7}+\cdots$$
83.7.b.c $38$ $19.094$ None None $$0$$ $$18$$ $$0$$ $$262$$
83.7.d.a $1640$ $19.094$ None None $$-41$$ $$-59$$ $$-41$$ $$-303$$
83.8.a.a $21$ $25.928$ None None $$-17$$ $$-95$$ $$-502$$ $$-3273$$ $-$
83.8.a.b $27$ $25.928$ None None $$23$$ $$67$$ $$748$$ $$1529$$ $+$
83.8.c.a $1920$ $25.928$ None None $$-47$$ $$-13$$ $$-287$$ $$1703$$
83.9.b.a $3$ $33.812$ 3.3.2241.1 $$\Q(\sqrt{-83})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-47\beta _{1}-2\beta _{2})q^{3}+2^{8}q^{4}+(-846\beta _{1}+\cdots)q^{7}+\cdots$$
83.9.b.b $52$ $33.812$ None None $$0$$ $$-114$$ $$0$$ $$2028$$
83.9.d.a $2200$ $33.812$ None None $$-41$$ $$73$$ $$-41$$ $$-2069$$
83.10.a.a $28$ $42.748$ None None $$-49$$ $$-317$$ $$-3467$$ $$-13836$$ $+$
83.10.a.b $34$ $42.748$ None None $$31$$ $$169$$ $$2783$$ $$19778$$ $-$
83.10.c.a $2480$ $42.748$ None None $$-23$$ $$107$$ $$643$$ $$-5983$$
83.11.b.a $3$ $52.735$ 3.3.2241.1 $$\Q(\sqrt{-83})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-139\beta _{1}+6\beta _{2})q^{3}+2^{10}q^{4}+(5922\beta _{1}+\cdots)q^{7}+\cdots$$
83.11.b.b $66$ $52.735$ None None $$0$$ $$42$$ $$0$$ $$-22288$$
83.11.d.a $2760$ $52.735$ None None $$-41$$ $$-83$$ $$-41$$ $$22247$$
83.12.a.a $34$ $63.772$ None None $$-41$$ $$-719$$ $$-19862$$ $$-97477$$ $-$
83.12.a.b $40$ $63.772$ None None $$119$$ $$739$$ $$11388$$ $$137821$$ $+$
83.12.c.a $3040$ $63.772$ None None $$-71$$ $$-565$$ $$-1227$$ $$-6897$$
83.13.b.a $1$ $75.861$ $$\Q$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$-617$$ $$0$$ $$-231577$$ $$q-617q^{3}+2^{12}q^{4}-231577q^{7}+\cdots$$
83.13.b.b $2$ $75.861$ $$\Q(\sqrt{249})$$ $$\Q(\sqrt{-83})$$ None $$0$$ $$617$$ $$0$$ $$231577$$ $$q+(294-29\beta )q^{3}+2^{12}q^{4}+(116246+\cdots)q^{7}+\cdots$$
83.13.b.c $80$ $75.861$ None None $$0$$ $$918$$ $$0$$ $$103918$$
83.14.a.a $42$ $89.002$ None None $$-193$$ $$-2057$$ $$-78072$$ $$-907547$$ $+$
83.14.a.b $48$ $89.002$ None None $$127$$ $$2317$$ $$78178$$ $$739539$$ $-$
83.15.b.a $3$ $103.193$ 3.3.2241.1 $$\Q(\sqrt{-83})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-63\beta _{1}+152\beta _{2})q^{3}+2^{14}q^{4}+\cdots$$
83.15.b.b $94$ $103.193$ None None $$0$$ $$-2238$$ $$0$$ $$-386388$$
83.16.a.a $48$ $118.436$ None None $$-473$$ $$-5843$$ $$-442447$$ $$-7927854$$ $-$
83.16.a.b $54$ $118.436$ None None $$167$$ $$7279$$ $$338803$$ $$3601748$$ $+$
83.18.a.a $55$ $152.074$ None None $$-241$$ $$-11321$$ $$-1009352$$ $$-50694303$$ $+$
83.18.a.b $61$ $152.074$ None None $$1039$$ $$28045$$ $$2896898$$ $$30012911$$ $-$
83.20.a.a $62$ $189.918$ None None $$-1481$$ $$-94199$$ $$-6266132$$ $$-202919777$$ $-$
83.20.a.b $68$ $189.918$ None None $$1079$$ $$23899$$ $$13265118$$ $$362030721$$ $+$