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Galois conjugate representations are grouped into single lines.
| Label | Dimension | Conductor | Artin stem field | $G$ | Ind | $\chi(c)$ |
|---|---|---|---|---|---|---|
| 3.229.4t5.a.a | $3$ | $ 229 $ | 4.0.229.1 | $S_4$ | $1$ | $-1$ |
| 3.257.4t5.a.a | $3$ | $ 257 $ | 4.0.257.1 | $S_4$ | $1$ | $-1$ |
| 3.283.4t5.b.a | $3$ | $ 283 $ | 4.2.283.1 | $S_4$ | $1$ | $1$ |
| 3.331.4t5.a.a | $3$ | $ 331 $ | 4.2.331.1 | $S_4$ | $1$ | $1$ |
| 3.491.4t5.b.a | $3$ | $ 491 $ | 4.2.491.1 | $S_4$ | $1$ | $1$ |
| 3.563.4t5.b.a | $3$ | $ 563 $ | 4.2.563.1 | $S_4$ | $1$ | $1$ |
| 3.592.4t5.a.a | $3$ | $ 2^{4} \cdot 37 $ | 4.0.592.1 | $S_4$ | $1$ | $-1$ |
| 3.643.4t5.a.a | $3$ | $ 643 $ | 4.2.643.1 | $S_4$ | $1$ | $1$ |
| 3.688.4t5.b.a | $3$ | $ 2^{4} \cdot 43 $ | 4.2.688.1 | $S_4$ | $1$ | $1$ |
| 3.697.4t5.a.a | $3$ | $ 17 \cdot 41 $ | 4.0.697.1 | $S_4$ | $1$ | $-1$ |
| 3.731.4t5.a.a | $3$ | $ 17 \cdot 43 $ | 4.2.731.1 | $S_4$ | $1$ | $1$ |
| 3.751.4t5.a.a | $3$ | $ 751 $ | 4.2.751.1 | $S_4$ | $1$ | $1$ |
| 3.761.4t5.a.a | $3$ | $ 761 $ | 4.0.761.1 | $S_4$ | $1$ | $-1$ |
| 3.788.4t5.a.a | $3$ | $ 2^{2} \cdot 197 $ | 4.0.788.1 | $S_4$ | $1$ | $-1$ |
| 3.848.4t5.b.a | $3$ | $ 2^{4} \cdot 53 $ | 4.2.848.1 | $S_4$ | $1$ | $1$ |
| 3.892.4t5.a.a | $3$ | $ 2^{2} \cdot 223 $ | 4.0.892.1 | $S_4$ | $1$ | $-1$ |
| 3.976.4t5.b.a | $3$ | $ 2^{4} \cdot 61 $ | 4.2.976.1 | $S_4$ | $1$ | $1$ |
| 3.985.4t5.a.a | $3$ | $ 5 \cdot 197 $ | 4.0.985.1 | $S_4$ | $1$ | $-1$ |
| 3.1016.4t5.a.a | $3$ | $ 2^{3} \cdot 127 $ | 4.0.1016.1 | $S_4$ | $1$ | $-1$ |
| 3.1076.4t5.a.a | $3$ | $ 2^{2} \cdot 269 $ | 4.0.1076.1 | $S_4$ | $1$ | $-1$ |
| 3.1099.4t5.a.a | $3$ | $ 7 \cdot 157 $ | 4.2.1099.1 | $S_4$ | $1$ | $1$ |
| 3.1107.4t5.a.a | $3$ | $ 3^{3} \cdot 41 $ | 4.2.1107.1 | $S_4$ | $1$ | $1$ |
| 3.1129.4t5.a.a | $3$ | $ 1129 $ | 4.0.1129.1 | $S_4$ | $1$ | $-1$ |
| 3.1192.4t5.a.a | $3$ | $ 2^{3} \cdot 149 $ | 4.2.1192.1 | $S_4$ | $1$ | $1$ |
| 3.1229.4t5.a.a | $3$ | $ 1229 $ | 4.0.1229.1 | $S_4$ | $1$ | $-1$ |
| 3.1255.4t5.a.a | $3$ | $ 5 \cdot 251 $ | 4.2.1255.1 | $S_4$ | $1$ | $1$ |
| 3.1257.4t5.a.a | $3$ | $ 3 \cdot 419 $ | 4.0.1257.1 | $S_4$ | $1$ | $-1$ |
| 3.1264.4t5.a.a | $3$ | $ 2^{4} \cdot 79 $ | 4.0.1264.1 | $S_4$ | $1$ | $-1$ |
| 3.1328.4t5.b.a | $3$ | $ 2^{4} \cdot 83 $ | 4.2.1328.1 | $S_4$ | $1$ | $1$ |
| 3.1371.4t5.a.a | $3$ | $ 3 \cdot 457 $ | 4.2.1371.1 | $S_4$ | $1$ | $1$ |
| 3.1384.4t5.a.a | $3$ | $ 2^{3} \cdot 173 $ | 4.0.1384.1 | $S_4$ | $1$ | $-1$ |
| 3.1396.4t5.a.a | $3$ | $ 2^{2} \cdot 349 $ | 4.0.1396.1 | $S_4$ | $1$ | $-1$ |
| 3.1399.4t5.a.a | $3$ | $ 1399 $ | 4.2.1399.1 | $S_4$ | $1$ | $1$ |
| 3.1423.4t5.a.a | $3$ | $ 1423 $ | 4.2.1423.1 | $S_4$ | $1$ | $1$ |
| 3.1424.4t5.a.a | $3$ | $ 2^{4} \cdot 89 $ | 4.2.1424.1 | $S_4$ | $1$ | $1$ |
| 3.1436.4t5.a.a | $3$ | $ 2^{2} \cdot 359 $ | 4.0.1436.1 | $S_4$ | $1$ | $-1$ |
| 3.1444.6t8.a.a | $3$ | $ 2^{2} \cdot 19^{2}$ | 4.2.27436.1 | $S_4$ | $1$ | $-1$ |
| 3.1456.4t5.b.a | $3$ | $ 2^{4} \cdot 7 \cdot 13 $ | 4.2.1456.1 | $S_4$ | $1$ | $1$ |
| 3.1472.4t5.b.a | $3$ | $ 2^{6} \cdot 23 $ | 4.2.1472.1 | $S_4$ | $1$ | $1$ |
| 3.1489.4t5.a.a | $3$ | $ 1489 $ | 4.0.1489.1 | $S_4$ | $1$ | $-1$ |
| 3.1492.4t5.a.a | $3$ | $ 2^{2} \cdot 373 $ | 4.0.1492.1 | $S_4$ | $1$ | $-1$ |
| 3.1509.4t5.a.a | $3$ | $ 3 \cdot 503 $ | 4.0.1509.1 | $S_4$ | $1$ | $-1$ |
| 3.1556.4t5.a.a | $3$ | $ 2^{2} \cdot 389 $ | 4.0.1556.1 | $S_4$ | $1$ | $-1$ |
| 3.1588.4t5.a.a | $3$ | $ 2^{2} \cdot 397 $ | 4.2.1588.1 | $S_4$ | $1$ | $1$ |
| 3.1593.4t5.a.a | $3$ | $ 3^{3} \cdot 59 $ | 4.0.1593.1 | $S_4$ | $1$ | $-1$ |
| 3.1616.4t5.a.a | $3$ | $ 2^{4} \cdot 101 $ | 4.0.1616.1 | $S_4$ | $1$ | $-1$ |
| 3.1732.4t5.a.a | $3$ | $ 2^{2} \cdot 433 $ | 4.2.1732.1 | $S_4$ | $1$ | $1$ |
| 3.1765.4t5.a.a | $3$ | $ 5 \cdot 353 $ | 4.0.1765.1 | $S_4$ | $1$ | $-1$ |
| 3.1791.4t5.b.a | $3$ | $ 3^{2} \cdot 199 $ | 4.2.1791.1 | $S_4$ | $1$ | $1$ |
| 3.1823.4t5.a.a | $3$ | $ 1823 $ | 4.2.1823.1 | $S_4$ | $1$ | $1$ |