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Dimension Conductor Group Root number Parity
Smallest permutation Ramified Unramified primes Ramified prime count Frobenius-Schur
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Galois conjugate representations are grouped into single lines.
Label Dimension Conductor Artin stem field $G$ Ind $\chi(c)$
1.5.4t1.a.a 1.5.4t1.a.b $1$ $ 5 $ \(\Q(\zeta_{5})\) $C_4$ $0$ $-1$
1.13.4t1.a.a 1.13.4t1.a.b $1$ $ 13 $ 4.0.2197.1 $C_4$ $0$ $-1$
1.15.4t1.a.a 1.15.4t1.a.b $1$ $ 3 \cdot 5 $ \(\Q(\zeta_{15})^+\) $C_4$ $0$ $1$
1.16.4t1.a.a 1.16.4t1.a.b $1$ $ 2^{4}$ \(\Q(\zeta_{16})^+\) $C_4$ $0$ $1$
1.16.4t1.b.a 1.16.4t1.b.b $1$ $ 2^{4}$ 4.0.2048.2 $C_4$ $0$ $-1$
1.17.4t1.a.a 1.17.4t1.a.b $1$ $ 17 $ 4.4.4913.1 $C_4$ $0$ $1$
1.20.4t1.a.a 1.20.4t1.a.b $1$ $ 2^{2} \cdot 5 $ \(\Q(\zeta_{20})^+\) $C_4$ $0$ $1$
1.29.4t1.a.a 1.29.4t1.a.b $1$ $ 29 $ 4.0.24389.1 $C_4$ $0$ $-1$
1.35.4t1.a.a 1.35.4t1.a.b $1$ $ 5 \cdot 7 $ 4.4.6125.1 $C_4$ $0$ $1$
1.37.4t1.a.a 1.37.4t1.a.b $1$ $ 37 $ 4.0.50653.1 $C_4$ $0$ $-1$
1.39.4t1.a.a 1.39.4t1.a.b $1$ $ 3 \cdot 13 $ 4.4.19773.1 $C_4$ $0$ $1$
1.40.4t1.a.a 1.40.4t1.a.b $1$ $ 2^{3} \cdot 5 $ 4.4.8000.1 $C_4$ $0$ $1$
1.40.4t1.b.a 1.40.4t1.b.b $1$ $ 2^{3} \cdot 5 $ 4.0.8000.2 $C_4$ $0$ $-1$
1.41.4t1.a.a 1.41.4t1.a.b $1$ $ 41 $ 4.4.68921.1 $C_4$ $0$ $1$
1.48.4t1.a.a 1.48.4t1.a.b $1$ $ 2^{4} \cdot 3 $ 4.4.18432.1 $C_4$ $0$ $1$
1.48.4t1.b.a 1.48.4t1.b.b $1$ $ 2^{4} \cdot 3 $ 4.0.18432.2 $C_4$ $0$ $-1$
1.51.4t1.a.a 1.51.4t1.a.b $1$ $ 3 \cdot 17 $ 4.0.44217.1 $C_4$ $0$ $-1$
1.52.4t1.a.a 1.52.4t1.a.b $1$ $ 2^{2} \cdot 13 $ 4.4.35152.1 $C_4$ $0$ $1$
1.53.4t1.a.a 1.53.4t1.a.b $1$ $ 53 $ 4.0.148877.1 $C_4$ $0$ $-1$
1.55.4t1.a.a 1.55.4t1.a.b $1$ $ 5 \cdot 11 $ 4.4.15125.1 $C_4$ $0$ $1$
1.60.4t1.a.a 1.60.4t1.a.b $1$ $ 2^{2} \cdot 3 \cdot 5 $ 4.0.18000.1 $C_4$ $0$ $-1$
1.61.4t1.a.a 1.61.4t1.a.b $1$ $ 61 $ 4.0.226981.1 $C_4$ $0$ $-1$
1.65.4t1.a.a 1.65.4t1.a.b $1$ $ 5 \cdot 13 $ 4.0.21125.1 $C_4$ $0$ $-1$
1.65.4t1.b.a 1.65.4t1.b.b $1$ $ 5 \cdot 13 $ 4.0.54925.1 $C_4$ $0$ $-1$
1.65.4t1.c.a 1.65.4t1.c.b $1$ $ 5 \cdot 13 $ 4.4.274625.2 $C_4$ $0$ $1$
1.65.4t1.d.a 1.65.4t1.d.b $1$ $ 5 \cdot 13 $ 4.4.274625.1 $C_4$ $0$ $1$
1.68.4t1.a.a 1.68.4t1.a.b $1$ $ 2^{2} \cdot 17 $ 4.0.78608.1 $C_4$ $0$ $-1$
1.73.4t1.a.a 1.73.4t1.a.b $1$ $ 73 $ 4.4.389017.1 $C_4$ $0$ $1$
1.80.4t1.a.a 1.80.4t1.a.b $1$ $ 2^{4} \cdot 5 $ 4.4.51200.1 $C_4$ $0$ $1$
1.80.4t1.b.a 1.80.4t1.b.b $1$ $ 2^{4} \cdot 5 $ 4.0.51200.2 $C_4$ $0$ $-1$
1.80.4t1.c.a 1.80.4t1.c.b $1$ $ 2^{4} \cdot 5 $ 4.4.256000.1 $C_4$ $0$ $1$
1.80.4t1.d.a 1.80.4t1.d.b $1$ $ 2^{4} \cdot 5 $ 4.0.256000.4 $C_4$ $0$ $-1$
1.80.4t1.e.a 1.80.4t1.e.b $1$ $ 2^{4} \cdot 5 $ 4.4.256000.2 $C_4$ $0$ $1$
1.80.4t1.f.a 1.80.4t1.f.b $1$ $ 2^{4} \cdot 5 $ 4.0.256000.2 $C_4$ $0$ $-1$
1.85.4t1.a.a 1.85.4t1.a.b $1$ $ 5 \cdot 17 $ 4.4.122825.1 $C_4$ $0$ $1$
1.85.4t1.b.a 1.85.4t1.b.b $1$ $ 5 \cdot 17 $ 4.0.614125.1 $C_4$ $0$ $-1$
1.85.4t1.c.a 1.85.4t1.c.b $1$ $ 5 \cdot 17 $ 4.0.614125.2 $C_4$ $0$ $-1$
1.85.4t1.d.a 1.85.4t1.d.b $1$ $ 5 \cdot 17 $ 4.0.36125.1 $C_4$ $0$ $-1$
1.87.4t1.a.a 1.87.4t1.a.b $1$ $ 3 \cdot 29 $ 4.4.219501.1 $C_4$ $0$ $1$
1.89.4t1.a.a 1.89.4t1.a.b $1$ $ 89 $ 4.4.704969.1 $C_4$ $0$ $1$
1.91.4t1.a.a 1.91.4t1.a.b $1$ $ 7 \cdot 13 $ 4.4.107653.1 $C_4$ $0$ $1$
1.95.4t1.a.a 1.95.4t1.a.b $1$ $ 5 \cdot 19 $ 4.4.45125.1 $C_4$ $0$ $1$
1.97.4t1.a.a 1.97.4t1.a.b $1$ $ 97 $ 4.4.912673.1 $C_4$ $0$ $1$
1.101.4t1.a.a 1.101.4t1.a.b $1$ $ 101 $ 4.0.1030301.1 $C_4$ $0$ $-1$
1.104.4t1.a.a 1.104.4t1.a.b $1$ $ 2^{3} \cdot 13 $ 4.4.140608.1 $C_4$ $0$ $1$
1.104.4t1.b.a 1.104.4t1.b.b $1$ $ 2^{3} \cdot 13 $ 4.0.140608.2 $C_4$ $0$ $-1$
1.105.4t1.a.a 1.105.4t1.a.b $1$ $ 3 \cdot 5 \cdot 7 $ 4.0.55125.1 $C_4$ $0$ $-1$
1.109.4t1.a.a 1.109.4t1.a.b $1$ $ 109 $ 4.0.1295029.1 $C_4$ $0$ $-1$
1.111.4t1.a.a 1.111.4t1.a.b $1$ $ 3 \cdot 37 $ 4.4.455877.1 $C_4$ $0$ $1$
1.112.4t1.a.a 1.112.4t1.a.b $1$ $ 2^{4} \cdot 7 $ 4.4.100352.1 $C_4$ $0$ $1$
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