Properties

Label 6003.2.a.n
Level 6003
Weight 2
Character orbit 6003.a
Self dual Yes
Analytic conductor 47.934
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\ldots,\beta_{11}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + \beta_{1} q^{2} + ( 1 - \beta_{4} - \beta_{6} + \beta_{8} ) q^{4} + ( 1 + \beta_{8} ) q^{5} + ( -1 + \beta_{1} + \beta_{6} - \beta_{10} ) q^{7} + ( \beta_{1} - \beta_{2} + \beta_{3} + \beta_{4} + \beta_{5} ) q^{8} +O(q^{10})\) \( q + \beta_{1} q^{2} + ( 1 - \beta_{4} - \beta_{6} + \beta_{8} ) q^{4} + ( 1 + \beta_{8} ) q^{5} + ( -1 + \beta_{1} + \beta_{6} - \beta_{10} ) q^{7} + ( \beta_{1} - \beta_{2} + \beta_{3} + \beta_{4} + \beta_{5} ) q^{8} + ( -1 + 2 \beta_{1} + \beta_{3} + 2 \beta_{4} + 2 \beta_{5} + \beta_{6} + \beta_{10} + \beta_{11} ) q^{10} + ( 1 + \beta_{2} - \beta_{5} - \beta_{10} ) q^{11} + ( -2 + \beta_{1} + \beta_{3} + \beta_{6} + 2 \beta_{9} - \beta_{10} - \beta_{11} ) q^{13} + ( 2 - 2 \beta_{1} + \beta_{2} - \beta_{4} - \beta_{6} - \beta_{7} ) q^{14} + ( 1 - \beta_{2} + \beta_{5} - \beta_{6} - \beta_{7} + \beta_{8} - \beta_{9} + \beta_{10} ) q^{16} + ( 2 + \beta_{3} - \beta_{5} + \beta_{6} + \beta_{7} ) q^{17} + ( -1 + \beta_{1} + \beta_{2} + \beta_{3} + 2 \beta_{4} + 2 \beta_{5} + \beta_{6} + \beta_{7} + \beta_{10} + \beta_{11} ) q^{19} + ( 2 - \beta_{2} - \beta_{4} + 2 \beta_{5} - 2 \beta_{6} + 3 \beta_{8} + \beta_{10} ) q^{20} + ( 1 - \beta_{1} + 2 \beta_{2} - 2 \beta_{3} - 2 \beta_{4} - \beta_{5} - 2 \beta_{6} - \beta_{7} - \beta_{9} - \beta_{10} ) q^{22} + q^{23} + ( 1 - \beta_{4} - \beta_{5} - \beta_{6} + \beta_{7} + 3 \beta_{8} - \beta_{9} ) q^{25} + ( 1 - \beta_{1} + \beta_{2} - 2 \beta_{4} + \beta_{6} - 2 \beta_{7} + 2 \beta_{9} - \beta_{10} ) q^{26} + ( -3 + 2 \beta_{1} - \beta_{2} + \beta_{3} + 2 \beta_{4} + \beta_{6} + \beta_{7} - \beta_{8} + \beta_{9} - \beta_{11} ) q^{28} + q^{29} + ( 2 + \beta_{2} + \beta_{3} + \beta_{6} ) q^{31} + ( 2 \beta_{1} - \beta_{2} + 2 \beta_{3} + 2 \beta_{4} + 2 \beta_{5} + 2 \beta_{6} + 2 \beta_{7} + 2 \beta_{8} + 2 \beta_{10} + \beta_{11} ) q^{32} + ( 1 - \beta_{3} - 3 \beta_{4} - 3 \beta_{5} - \beta_{6} - 2 \beta_{7} - \beta_{8} - \beta_{10} - \beta_{11} ) q^{34} + ( 2 \beta_{1} + \beta_{3} + 2 \beta_{4} + 3 \beta_{6} + 2 \beta_{7} + \beta_{11} ) q^{35} + ( -\beta_{2} - \beta_{4} - 2 \beta_{6} - \beta_{7} - 2 \beta_{10} ) q^{37} + ( 1 - \beta_{1} + \beta_{2} - 3 \beta_{3} - \beta_{4} + \beta_{5} - 3 \beta_{6} - \beta_{7} + 3 \beta_{8} - \beta_{9} ) q^{38} + ( -1 + 5 \beta_{1} - 3 \beta_{2} + 2 \beta_{3} + 3 \beta_{4} + 3 \beta_{5} + \beta_{7} + \beta_{8} + \beta_{10} ) q^{40} + ( -1 + \beta_{1} - \beta_{2} + \beta_{3} + \beta_{6} - \beta_{7} - 2 \beta_{8} + 2 \beta_{9} - 3 \beta_{10} - 2 \beta_{11} ) q^{41} + ( -2 \beta_{1} - \beta_{3} - 3 \beta_{4} - 3 \beta_{5} - 4 \beta_{6} - \beta_{7} - \beta_{9} - \beta_{10} - 2 \beta_{11} ) q^{43} + ( -3 + \beta_{1} - \beta_{3} + 2 \beta_{4} + 2 \beta_{5} + 2 \beta_{7} - 2 \beta_{8} - \beta_{9} ) q^{44} + \beta_{1} q^{46} + ( 5 - \beta_{1} + \beta_{2} - 2 \beta_{4} - \beta_{7} - \beta_{9} + 2 \beta_{11} ) q^{47} + ( 1 - 3 \beta_{1} - \beta_{3} + \beta_{4} - \beta_{5} - \beta_{6} + 2 \beta_{10} + \beta_{11} ) q^{49} + ( 2 \beta_{1} + \beta_{3} + 3 \beta_{4} + 3 \beta_{5} - \beta_{6} - \beta_{7} - \beta_{8} - 2 \beta_{9} + 2 \beta_{10} + 2 \beta_{11} ) q^{50} + ( -2 + 4 \beta_{1} - 2 \beta_{2} + 3 \beta_{3} + 3 \beta_{4} + 7 \beta_{6} + \beta_{7} - 2 \beta_{8} + 2 \beta_{9} - \beta_{10} ) q^{52} + ( 5 + \beta_{2} - \beta_{4} - \beta_{5} - 2 \beta_{6} - 2 \beta_{7} ) q^{53} + ( \beta_{1} + \beta_{2} + 4 \beta_{4} + 3 \beta_{6} + 2 \beta_{7} + \beta_{8} - \beta_{9} + \beta_{10} + \beta_{11} ) q^{55} + ( 2 - 2 \beta_{1} - 3 \beta_{3} - 3 \beta_{4} - \beta_{5} - 2 \beta_{6} + 2 \beta_{8} - \beta_{9} + \beta_{10} + \beta_{11} ) q^{56} + \beta_{1} q^{58} + ( -1 + 4 \beta_{1} + \beta_{2} - 2 \beta_{3} + 2 \beta_{6} + \beta_{7} + \beta_{9} - 2 \beta_{10} + \beta_{11} ) q^{59} + ( 1 + 2 \beta_{1} - 2 \beta_{4} - 2 \beta_{5} + \beta_{6} + \beta_{7} - \beta_{10} + \beta_{11} ) q^{61} + ( 2 \beta_{1} - \beta_{4} - \beta_{5} + \beta_{6} - \beta_{7} + \beta_{9} - 2 \beta_{10} - \beta_{11} ) q^{62} + ( 2 \beta_{1} + \beta_{3} + \beta_{4} + \beta_{5} + \beta_{6} + \beta_{8} + 2 \beta_{9} + \beta_{10} + \beta_{11} ) q^{64} + ( -2 + 3 \beta_{1} - 2 \beta_{2} + 2 \beta_{3} - \beta_{4} - \beta_{5} + 2 \beta_{6} + \beta_{7} - 2 \beta_{8} + 4 \beta_{9} - 3 \beta_{10} - 3 \beta_{11} ) q^{65} + ( -3 - \beta_{2} + \beta_{3} + 5 \beta_{4} + 5 \beta_{5} + 2 \beta_{6} - 2 \beta_{8} - \beta_{9} + 2 \beta_{10} + 2 \beta_{11} ) q^{67} + ( \beta_{1} - 2 \beta_{2} + 2 \beta_{3} - 2 \beta_{4} - 2 \beta_{5} + 2 \beta_{6} - 2 \beta_{8} + 3 \beta_{9} - 3 \beta_{10} - 2 \beta_{11} ) q^{68} + ( 4 - 4 \beta_{1} + 2 \beta_{2} - 3 \beta_{3} - 4 \beta_{4} - 2 \beta_{5} - 4 \beta_{6} - 3 \beta_{7} + \beta_{8} - \beta_{9} + \beta_{10} ) q^{70} + ( -3 + 2 \beta_{1} - \beta_{2} + 2 \beta_{3} + 3 \beta_{4} + 4 \beta_{6} - \beta_{8} + 2 \beta_{9} + \beta_{10} ) q^{71} + ( 2 - 3 \beta_{1} - 2 \beta_{3} - 4 \beta_{4} - 4 \beta_{5} - 4 \beta_{6} - 2 \beta_{7} + \beta_{8} + \beta_{9} - 3 \beta_{10} - 3 \beta_{11} ) q^{73} + ( 2 - \beta_{2} - 3 \beta_{4} - 5 \beta_{6} - \beta_{7} + 2 \beta_{8} - 2 \beta_{9} - \beta_{11} ) q^{74} + ( -4 + 4 \beta_{1} + 8 \beta_{4} + 6 \beta_{5} + \beta_{6} + 2 \beta_{7} - \beta_{8} - 2 \beta_{9} + 2 \beta_{10} + 3 \beta_{11} ) q^{76} + ( 3 + \beta_{1} + \beta_{2} - 2 \beta_{3} - \beta_{4} - 2 \beta_{5} + \beta_{6} + 2 \beta_{7} + 3 \beta_{8} - \beta_{9} + 2 \beta_{10} + 2 \beta_{11} ) q^{77} + ( 1 + \beta_{1} - 2 \beta_{3} - \beta_{4} - \beta_{5} - 2 \beta_{7} - 2 \beta_{8} - 3 \beta_{10} - 2 \beta_{11} ) q^{79} + ( 9 - 2 \beta_{4} + \beta_{5} - 5 \beta_{6} - 2 \beta_{7} + 3 \beta_{8} - 3 \beta_{9} + 3 \beta_{10} + 2 \beta_{11} ) q^{80} + ( 3 - 3 \beta_{1} + 2 \beta_{2} - \beta_{3} - 6 \beta_{4} - 2 \beta_{5} - 2 \beta_{6} - 3 \beta_{7} + \beta_{9} - 2 \beta_{10} - \beta_{11} ) q^{82} + ( -1 + 2 \beta_{1} - 2 \beta_{2} + \beta_{3} + \beta_{4} + 2 \beta_{5} - \beta_{6} + 3 \beta_{7} + \beta_{8} - 2 \beta_{9} + \beta_{10} - 2 \beta_{11} ) q^{83} + ( \beta_{1} - \beta_{2} + 2 \beta_{3} + \beta_{4} - 3 \beta_{5} + 5 \beta_{6} + 2 \beta_{7} + 2 \beta_{8} + \beta_{9} - \beta_{10} - \beta_{11} ) q^{85} + ( 1 - \beta_{1} - \beta_{4} - 2 \beta_{5} - \beta_{6} + \beta_{7} - 3 \beta_{8} - 2 \beta_{9} - 2 \beta_{10} ) q^{86} + ( 1 - 6 \beta_{1} + \beta_{2} - 4 \beta_{3} + \beta_{4} + \beta_{5} - 5 \beta_{6} + \beta_{7} - 3 \beta_{9} + 3 \beta_{10} + \beta_{11} ) q^{88} + ( 3 - 3 \beta_{1} - \beta_{2} - 3 \beta_{4} - 4 \beta_{6} - \beta_{9} - 2 \beta_{10} - 2 \beta_{11} ) q^{89} + ( 1 - \beta_{1} + \beta_{2} - \beta_{3} - 3 \beta_{4} - 2 \beta_{6} + 2 \beta_{7} + 3 \beta_{8} + \beta_{9} + 2 \beta_{10} ) q^{91} + ( 1 - \beta_{4} - \beta_{6} + \beta_{8} ) q^{92} + ( -2 + 7 \beta_{1} - 4 \beta_{2} + 3 \beta_{3} - 3 \beta_{5} + 2 \beta_{6} + \beta_{7} + 2 \beta_{9} - 3 \beta_{10} - 4 \beta_{11} ) q^{94} + ( -3 + 5 \beta_{1} + \beta_{2} - \beta_{3} + 3 \beta_{4} + 2 \beta_{5} - \beta_{6} + \beta_{7} - 2 \beta_{9} + \beta_{10} + \beta_{11} ) q^{95} + ( -2 - \beta_{2} + 2 \beta_{4} + \beta_{5} + \beta_{6} + \beta_{7} + 2 \beta_{8} - 3 \beta_{9} + \beta_{10} + \beta_{11} ) q^{97} + ( -8 + \beta_{1} - \beta_{2} + 4 \beta_{4} + 4 \beta_{6} + 3 \beta_{7} - \beta_{8} + 2 \beta_{10} + \beta_{11} ) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 3q^{2} + 11q^{4} + 16q^{5} - 7q^{7} + 9q^{8} + O(q^{10}) \) \( 12q + 3q^{2} + 11q^{4} + 16q^{5} - 7q^{7} + 9q^{8} + 6q^{11} - 15q^{13} + 8q^{14} + 17q^{16} + 18q^{17} - 6q^{19} + 39q^{20} - 5q^{22} + 12q^{23} + 14q^{25} + 3q^{26} - 19q^{28} + 12q^{29} + 16q^{31} + 21q^{32} - 7q^{34} + 11q^{35} - q^{37} + 24q^{38} + 30q^{40} - 3q^{41} - 23q^{43} - 23q^{44} + 3q^{46} + 35q^{47} + 3q^{49} + 2q^{50} + 45q^{53} + 17q^{55} + 17q^{56} + 3q^{58} + 11q^{59} + 4q^{61} + 7q^{62} + 15q^{64} - 5q^{65} - 19q^{67} - q^{68} + 14q^{70} - 19q^{71} + 10q^{73} + 15q^{74} - 4q^{76} + 39q^{77} + 17q^{79} + 90q^{80} - 3q^{82} + 12q^{83} + 14q^{85} - 17q^{86} - 2q^{88} + 20q^{89} + 11q^{91} + 11q^{92} + 13q^{94} - 12q^{95} - 12q^{97} - 75q^{98} + O(q^{100}) \)

Basis of coefficient ring in terms of a root \(\nu\) of \(x^{12} - 3 x^{11} - 13 x^{10} + 41 x^{9} + 54 x^{8} - 188 x^{7} - 77 x^{6} + 342 x^{5} + 13 x^{4} - 215 x^{3} + 9 x^{2} + 37 x - 5\):

\(\beta_{0}\)\(=\)\( 1 \)
\(\beta_{1}\)\(=\)\( \nu \)
\(\beta_{2}\)\(=\)\((\)\( 69 \nu^{11} - 2268 \nu^{10} + 4126 \nu^{9} + 30343 \nu^{8} - 62480 \nu^{7} - 131017 \nu^{6} + 277030 \nu^{5} + 194815 \nu^{4} - 433403 \nu^{3} - 31183 \nu^{2} + 158295 \nu - 20718 \)\()/6469\)
\(\beta_{3}\)\(=\)\((\)\( -127 \nu^{11} - 607 \nu^{10} + 4875 \nu^{9} + 7810 \nu^{8} - 51132 \nu^{7} - 30082 \nu^{6} + 209382 \nu^{5} + 24036 \nu^{4} - 328362 \nu^{3} + 49707 \nu^{2} + 117880 \nu - 29932 \)\()/6469\)
\(\beta_{4}\)\(=\)\((\)\( -353 \nu^{11} - 210 \nu^{10} + 8049 \nu^{9} + 773 \nu^{8} - 63527 \nu^{7} + 13625 \nu^{6} + 210856 \nu^{5} - 84627 \nu^{4} - 276488 \nu^{3} + 135717 \nu^{2} + 84019 \nu - 25638 \)\()/6469\)
\(\beta_{5}\)\(=\)\((\)\( 549 \nu^{11} - 1451 \nu^{10} - 8798 \nu^{9} + 21760 \nu^{8} + 52179 \nu^{7} - 114560 \nu^{6} - 143208 \nu^{5} + 255406 \nu^{4} + 177916 \nu^{3} - 216607 \nu^{2} - 75949 \nu + 34852 \)\()/6469\)
\(\beta_{6}\)\(=\)\((\)\( -874 \nu^{11} + 2852 \nu^{10} + 10271 \nu^{9} - 37175 \nu^{8} - 32306 \nu^{7} + 154428 \nu^{6} + 1464 \nu^{5} - 218601 \nu^{4} + 86000 \nu^{3} + 34877 \nu^{2} - 19087 \nu + 23075 \)\()/6469\)
\(\beta_{7}\)\(=\)\((\)\( 1153 \nu^{11} - 2741 \nu^{10} - 16651 \nu^{9} + 36674 \nu^{8} + 84275 \nu^{7} - 163016 \nu^{6} - 182412 \nu^{5} + 282647 \nu^{4} + 156809 \nu^{3} - 153652 \nu^{2} - 43159 \nu + 10438 \)\()/6469\)
\(\beta_{8}\)\(=\)\((\)\( -1227 \nu^{11} + 2642 \nu^{10} + 18320 \nu^{9} - 36402 \nu^{8} - 95833 \nu^{7} + 168053 \nu^{6} + 212320 \nu^{5} - 303228 \nu^{4} - 190488 \nu^{3} + 177063 \nu^{2} + 64932 \nu - 21970 \)\()/6469\)
\(\beta_{9}\)\(=\)\((\)\( 1231 \nu^{11} - 3336 \nu^{10} - 16487 \nu^{9} + 44255 \nu^{8} + 73554 \nu^{7} - 190180 \nu^{6} - 130539 \nu^{5} + 291927 \nu^{4} + 89329 \nu^{3} - 89336 \nu^{2} - 43380 \nu - 10451 \)\()/6469\)
\(\beta_{10}\)\(=\)\((\)\( 2257 \nu^{11} - 6684 \nu^{10} - 28263 \nu^{9} + 88739 \nu^{8} + 106697 \nu^{7} - 383278 \nu^{6} - 103569 \nu^{5} + 605079 \nu^{4} - 88693 \nu^{3} - 238564 \nu^{2} + 63686 \nu + 8869 \)\()/6469\)
\(\beta_{11}\)\(=\)\((\)\( -2687 \nu^{11} + 10130 \nu^{10} + 28520 \nu^{9} - 134015 \nu^{8} - 63186 \nu^{7} + 578643 \nu^{6} - 126167 \nu^{5} - 926609 \nu^{4} + 441457 \nu^{3} + 391735 \nu^{2} - 161659 \nu - 20106 \)\()/6469\)
\(1\)\(=\)\(\beta_0\)
\(\nu\)\(=\)\(\beta_{1}\)
\(\nu^{2}\)\(=\)\(\beta_{8} - \beta_{6} - \beta_{4} + 3\)
\(\nu^{3}\)\(=\)\(\beta_{5} + \beta_{4} + \beta_{3} - \beta_{2} + 5 \beta_{1}\)
\(\nu^{4}\)\(=\)\(\beta_{10} - \beta_{9} + 7 \beta_{8} - \beta_{7} - 7 \beta_{6} + \beta_{5} - 6 \beta_{4} - \beta_{2} + 15\)
\(\nu^{5}\)\(=\)\(\beta_{11} + 2 \beta_{10} + 2 \beta_{8} + 2 \beta_{7} + 2 \beta_{6} + 10 \beta_{5} + 10 \beta_{4} + 10 \beta_{3} - 9 \beta_{2} + 30 \beta_{1}\)
\(\nu^{6}\)\(=\)\(\beta_{11} + 11 \beta_{10} - 8 \beta_{9} + 47 \beta_{8} - 10 \beta_{7} - 45 \beta_{6} + 11 \beta_{5} - 35 \beta_{4} + \beta_{3} - 10 \beta_{2} + 2 \beta_{1} + 86\)
\(\nu^{7}\)\(=\)\(10 \beta_{11} + 21 \beta_{10} + 3 \beta_{9} + 24 \beta_{8} + 20 \beta_{7} + 22 \beta_{6} + 78 \beta_{5} + 76 \beta_{4} + 78 \beta_{3} - 68 \beta_{2} + 192 \beta_{1} + 2\)
\(\nu^{8}\)\(=\)\(12 \beta_{11} + 90 \beta_{10} - 50 \beta_{9} + 314 \beta_{8} - 77 \beta_{7} - 283 \beta_{6} + 94 \beta_{5} - 209 \beta_{4} + 19 \beta_{3} - 81 \beta_{2} + 32 \beta_{1} + 527\)
\(\nu^{9}\)\(=\)\(74 \beta_{11} + 167 \beta_{10} + 43 \beta_{9} + 214 \beta_{8} + 148 \beta_{7} + 178 \beta_{6} + 559 \beta_{5} + 524 \beta_{4} + 565 \beta_{3} - 488 \beta_{2} + 1261 \beta_{1} + 40\)
\(\nu^{10}\)\(=\)\(99 \beta_{11} + 661 \beta_{10} - 284 \beta_{9} + 2098 \beta_{8} - 546 \beta_{7} - 1773 \beta_{6} + 724 \beta_{5} - 1281 \beta_{4} + 227 \beta_{3} - 622 \beta_{2} + 351 \beta_{1} + 3354\)
\(\nu^{11}\)\(=\)\(491 \beta_{11} + 1212 \beta_{10} + 431 \beta_{9} + 1715 \beta_{8} + 980 \beta_{7} + 1286 \beta_{6} + 3859 \beta_{5} + 3450 \beta_{4} + 3981 \beta_{3} - 3436 \beta_{2} + 8380 \beta_{1} + 515\)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
−2.52122
−1.89304
−1.65670
−0.724122
−0.613795
0.147789
0.431373
1.08419
1.49364
1.99588
2.58646
2.66955
−2.52122 0 4.35654 3.14716 0 −3.79117 −5.94135 0 −7.93467
1.2 −1.89304 0 1.58359 4.13664 0 2.17357 0.788273 0 −7.83081
1.3 −1.65670 0 0.744648 −1.18716 0 −3.31827 2.07974 0 1.96676
1.4 −0.724122 0 −1.47565 1.17886 0 −4.09140 2.51679 0 −0.853636
1.5 −0.613795 0 −1.62326 0.782514 0 3.32687 2.22394 0 −0.480303
1.6 0.147789 0 −1.97816 −0.429801 0 0.404424 −0.587929 0 −0.0635200
1.7 0.431373 0 −1.81392 3.65141 0 2.43060 −1.64522 0 1.57512
1.8 1.08419 0 −0.824542 −0.786014 0 −4.63453 −3.06233 0 −0.852185
1.9 1.49364 0 0.230961 1.29771 0 1.16738 −2.64231 0 1.93831
1.10 1.99588 0 1.98352 −2.38535 0 −0.101071 −0.0328940 0 −4.76086
1.11 2.58646 0 4.68978 3.69848 0 −0.298143 6.95702 0 9.56597
1.12 2.66955 0 5.12647 2.89555 0 −0.268248 8.34627 0 7.72982
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.12
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(23\) \(-1\)
\(29\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6003))\):

\(T_{2}^{12} - \cdots\)
\(T_{5}^{12} - \cdots\)