Properties

Label 6003.2.a.p
Level 6003
Weight 2
Character orbit 6003.a
Self dual Yes
Analytic conductor 47.934
Analytic rank 0
Dimension 14
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: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\ldots,\beta_{13}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + \beta_{1} q^{2} + ( 1 + \beta_{2} ) q^{4} -\beta_{11} q^{5} + ( \beta_{3} - \beta_{11} - \beta_{13} ) q^{7} + ( 1 + \beta_{1} + \beta_{3} + \beta_{4} ) q^{8} +O(q^{10})\) \( q + \beta_{1} q^{2} + ( 1 + \beta_{2} ) q^{4} -\beta_{11} q^{5} + ( \beta_{3} - \beta_{11} - \beta_{13} ) q^{7} + ( 1 + \beta_{1} + \beta_{3} + \beta_{4} ) q^{8} + ( -1 + \beta_{10} - \beta_{11} ) q^{10} + ( 1 + \beta_{6} ) q^{11} + ( 1 - \beta_{8} ) q^{13} + ( -\beta_{1} + 2 \beta_{2} + \beta_{5} + \beta_{10} - \beta_{11} - \beta_{13} ) q^{14} + ( \beta_{1} + \beta_{2} + \beta_{4} + \beta_{5} + \beta_{6} ) q^{16} + ( 1 - \beta_{1} + \beta_{3} - \beta_{4} - \beta_{6} - \beta_{8} - \beta_{11} - \beta_{13} ) q^{17} + ( \beta_{1} - \beta_{2} + \beta_{3} + \beta_{7} + \beta_{8} - \beta_{10} - \beta_{11} ) q^{19} + ( -2 \beta_{1} + \beta_{2} - \beta_{4} + \beta_{7} + \beta_{10} - \beta_{11} - \beta_{13} ) q^{20} + ( -1 + 3 \beta_{1} - \beta_{2} + \beta_{3} + \beta_{4} + \beta_{5} + \beta_{8} + \beta_{13} ) q^{22} + q^{23} + ( 2 \beta_{1} - \beta_{2} - \beta_{3} + \beta_{4} + \beta_{6} - \beta_{7} - \beta_{8} + \beta_{9} + \beta_{13} ) q^{25} + ( 1 + 2 \beta_{1} + \beta_{3} + \beta_{4} - \beta_{7} + \beta_{9} + \beta_{13} ) q^{26} + ( 2 \beta_{1} + \beta_{3} + \beta_{4} + \beta_{10} - \beta_{11} ) q^{28} + q^{29} + ( -3 - \beta_{3} - \beta_{7} - \beta_{9} + \beta_{10} ) q^{31} + ( 2 \beta_{1} + \beta_{3} + \beta_{4} + \beta_{5} + \beta_{6} - \beta_{7} + \beta_{8} + \beta_{13} ) q^{32} + ( \beta_{2} - \beta_{7} - \beta_{8} + \beta_{9} + \beta_{10} - \beta_{11} - \beta_{13} ) q^{34} + ( 2 - \beta_{1} + \beta_{2} + \beta_{3} - \beta_{5} - \beta_{6} + \beta_{7} - 2 \beta_{13} ) q^{35} + ( -1 - \beta_{1} - \beta_{2} - 2 \beta_{4} - \beta_{6} + \beta_{7} - \beta_{9} ) q^{37} + ( -1 - \beta_{1} + \beta_{2} - \beta_{3} + \beta_{5} + \beta_{6} + \beta_{8} - \beta_{9} + \beta_{10} - \beta_{12} ) q^{38} + ( -1 - \beta_{2} + 2 \beta_{3} - \beta_{4} - \beta_{6} + \beta_{7} + \beta_{8} - \beta_{10} - 2 \beta_{11} - \beta_{12} - 2 \beta_{13} ) q^{40} + ( 3 + \beta_{2} + \beta_{4} - \beta_{10} + \beta_{11} + \beta_{12} ) q^{41} + ( 1 + \beta_{2} - \beta_{4} - \beta_{5} - \beta_{6} + \beta_{7} + \beta_{8} - \beta_{10} - \beta_{11} - \beta_{13} ) q^{43} + ( 3 - \beta_{1} + 3 \beta_{2} - \beta_{3} + \beta_{4} + \beta_{5} + \beta_{6} - \beta_{9} ) q^{44} + \beta_{1} q^{46} + ( 2 + \beta_{1} - \beta_{2} - \beta_{5} + \beta_{6} - \beta_{10} + \beta_{11} - \beta_{12} ) q^{47} + ( 2 - \beta_{2} - \beta_{4} - 2 \beta_{5} + \beta_{7} - \beta_{8} - \beta_{11} + \beta_{12} ) q^{49} + ( 3 - 2 \beta_{1} - \beta_{4} - \beta_{5} - \beta_{6} - \beta_{7} - 2 \beta_{8} + \beta_{9} + \beta_{13} ) q^{50} + ( 2 + 3 \beta_{2} - \beta_{3} + \beta_{6} - \beta_{8} - \beta_{13} ) q^{52} + ( 2 - 2 \beta_{1} - \beta_{6} - \beta_{8} - \beta_{10} + \beta_{12} - \beta_{13} ) q^{53} + ( 1 - 2 \beta_{1} + \beta_{2} - \beta_{3} - \beta_{4} - 2 \beta_{5} - \beta_{6} - 2 \beta_{8} + \beta_{11} + \beta_{12} + \beta_{13} ) q^{55} + ( 5 + \beta_{1} + \beta_{2} - \beta_{5} + \beta_{6} + \beta_{7} - \beta_{10} - \beta_{11} + \beta_{13} ) q^{56} + \beta_{1} q^{58} + ( 3 - \beta_{1} - \beta_{2} - \beta_{5} - \beta_{6} + \beta_{7} - \beta_{9} - \beta_{10} + 2 \beta_{11} ) q^{59} + ( -2 + \beta_{2} - \beta_{3} + \beta_{4} + 2 \beta_{5} + \beta_{6} - \beta_{7} ) q^{61} + ( 1 - 2 \beta_{1} - \beta_{3} + \beta_{7} + \beta_{8} + 2 \beta_{12} + \beta_{13} ) q^{62} + ( 2 + 2 \beta_{1} - \beta_{2} + \beta_{4} + \beta_{6} - \beta_{9} + \beta_{11} + \beta_{12} + \beta_{13} ) q^{64} + ( -\beta_{3} + \beta_{6} + \beta_{10} - 2 \beta_{11} + \beta_{13} ) q^{65} + ( \beta_{1} - \beta_{2} - \beta_{3} - \beta_{5} + \beta_{6} - 2 \beta_{7} - \beta_{8} - \beta_{10} + \beta_{11} ) q^{67} + ( 1 - \beta_{1} + 2 \beta_{2} - \beta_{3} - \beta_{5} - \beta_{8} + \beta_{9} + \beta_{10} - \beta_{11} - \beta_{13} ) q^{68} + ( 1 - 2 \beta_{1} + 4 \beta_{2} - 2 \beta_{4} - 2 \beta_{6} + \beta_{7} - \beta_{11} - \beta_{12} - 3 \beta_{13} ) q^{70} + ( 4 + \beta_{1} - 2 \beta_{2} + \beta_{3} - \beta_{4} - \beta_{5} - \beta_{6} - \beta_{7} - \beta_{10} + \beta_{13} ) q^{71} + ( 3 \beta_{1} - \beta_{2} - \beta_{3} + \beta_{5} - \beta_{7} + \beta_{8} - \beta_{10} + \beta_{11} - \beta_{12} + \beta_{13} ) q^{73} + ( -1 - 2 \beta_{2} - \beta_{3} + \beta_{6} + 2 \beta_{8} + \beta_{13} ) q^{74} + ( -2 + 2 \beta_{1} - \beta_{2} + \beta_{3} + \beta_{4} + \beta_{7} + \beta_{8} + \beta_{10} + \beta_{12} + \beta_{13} ) q^{76} + ( 4 + \beta_{1} - 3 \beta_{2} + 4 \beta_{3} - \beta_{5} - \beta_{6} + \beta_{7} - 2 \beta_{10} - \beta_{13} ) q^{77} + ( -5 + \beta_{1} + \beta_{3} - \beta_{4} + \beta_{8} - \beta_{10} - \beta_{11} - 2 \beta_{12} - \beta_{13} ) q^{79} + ( -2 \beta_{1} + \beta_{2} - \beta_{3} - \beta_{4} - \beta_{6} - \beta_{10} - \beta_{12} - \beta_{13} ) q^{80} + ( -1 + 5 \beta_{1} + 3 \beta_{4} + \beta_{5} + \beta_{6} - 3 \beta_{7} - \beta_{9} + 4 \beta_{11} + \beta_{13} ) q^{82} + ( -3 \beta_{1} + \beta_{2} - 2 \beta_{4} + \beta_{5} - \beta_{6} - \beta_{7} - \beta_{9} + \beta_{10} - \beta_{11} - \beta_{12} - \beta_{13} ) q^{83} + ( 1 - \beta_{1} + 2 \beta_{2} - \beta_{3} + \beta_{4} - \beta_{5} + \beta_{6} + \beta_{7} + 3 \beta_{10} - \beta_{11} + \beta_{12} ) q^{85} + ( 1 - \beta_{1} + \beta_{2} - \beta_{3} - 2 \beta_{4} - \beta_{5} - 2 \beta_{6} + \beta_{7} - \beta_{9} + \beta_{10} - \beta_{12} - 2 \beta_{13} ) q^{86} + ( 7 \beta_{1} - \beta_{2} + 3 \beta_{3} + 4 \beta_{4} - \beta_{5} + \beta_{6} - \beta_{7} + \beta_{8} + \beta_{11} + \beta_{12} + \beta_{13} ) q^{88} + ( -2 + 3 \beta_{1} - \beta_{2} + 2 \beta_{4} + 2 \beta_{5} + \beta_{6} - 3 \beta_{7} + 2 \beta_{10} - 2 \beta_{11} - \beta_{12} ) q^{89} + ( -1 + 2 \beta_{1} + 2 \beta_{3} + 2 \beta_{7} + 3 \beta_{8} - \beta_{10} - \beta_{11} - \beta_{12} - \beta_{13} ) q^{91} + ( 1 + \beta_{2} ) q^{92} + ( 2 + 2 \beta_{1} - \beta_{4} - 2 \beta_{6} + 2 \beta_{7} + \beta_{8} + \beta_{9} - 2 \beta_{10} + 2 \beta_{11} + 2 \beta_{13} ) q^{94} + ( 5 + \beta_{1} - \beta_{2} + 2 \beta_{4} - \beta_{5} - \beta_{7} - \beta_{8} + \beta_{9} - \beta_{10} + 2 \beta_{11} ) q^{95} + ( 2 + 3 \beta_{1} + \beta_{2} + \beta_{5} + \beta_{7} + \beta_{8} + \beta_{9} - 2 \beta_{10} + 2 \beta_{13} ) q^{97} + ( -1 + \beta_{2} - 2 \beta_{3} - \beta_{4} + \beta_{5} - \beta_{6} - \beta_{7} + \beta_{8} + 2 \beta_{10} - \beta_{11} - \beta_{12} + \beta_{13} ) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{2} + 12q^{4} + 3q^{5} - 3q^{7} + 6q^{8} + O(q^{10}) \) \( 14q + 2q^{2} + 12q^{4} + 3q^{5} - 3q^{7} + 6q^{8} - 5q^{10} + 12q^{11} + 13q^{13} + 9q^{14} + 14q^{17} - 9q^{19} + 2q^{20} - 9q^{22} + 14q^{23} + 13q^{25} + 16q^{26} + 3q^{28} + 14q^{29} - 28q^{31} + 4q^{32} + 14q^{34} + 9q^{35} - 12q^{37} - 2q^{38} - 20q^{40} + 25q^{41} + 5q^{43} + 37q^{44} + 2q^{46} + 17q^{47} + 17q^{49} + 44q^{50} + 25q^{52} + 17q^{53} + q^{55} + 54q^{56} + 2q^{58} + 18q^{59} - 13q^{61} + 8q^{62} + 20q^{64} + 16q^{65} + 2q^{67} + 19q^{68} + 14q^{70} + 55q^{71} + 19q^{73} - 4q^{74} - 32q^{76} + 19q^{77} - 68q^{79} + 2q^{80} - 12q^{82} + 21q^{83} + 16q^{85} + 22q^{86} - 25q^{88} + 17q^{89} - 30q^{91} + 12q^{92} + 16q^{94} + 55q^{95} + 25q^{97} + 31q^{98} + O(q^{100}) \)

Basis of coefficient ring in terms of a root \(\nu\) of \(x^{14} - 2 x^{13} - 18 x^{12} + 34 x^{11} + 124 x^{10} - 216 x^{9} - 420 x^{8} + 647 x^{7} + 750 x^{6} - 939 x^{5} - 717 x^{4} + 604 x^{3} + 352 x^{2} - 128 x - 64\):

\(\beta_{0}\)\(=\)\( 1 \)
\(\beta_{1}\)\(=\)\( \nu \)
\(\beta_{2}\)\(=\)\( \nu^{2} - 3 \)
\(\beta_{3}\)\(=\)\((\)\( \nu^{13} - 2 \nu^{12} - 18 \nu^{11} + 34 \nu^{10} + 124 \nu^{9} - 216 \nu^{8} - 420 \nu^{7} + 647 \nu^{6} + 750 \nu^{5} - 939 \nu^{4} - 701 \nu^{3} + 604 \nu^{2} + 256 \nu - 128 \)\()/16\)
\(\beta_{4}\)\(=\)\((\)\( -\nu^{13} + 2 \nu^{12} + 18 \nu^{11} - 34 \nu^{10} - 124 \nu^{9} + 216 \nu^{8} + 420 \nu^{7} - 647 \nu^{6} - 750 \nu^{5} + 939 \nu^{4} + 717 \nu^{3} - 604 \nu^{2} - 336 \nu + 112 \)\()/16\)
\(\beta_{5}\)\(=\)\((\)\( -21 \nu^{13} + 142 \nu^{12} + 210 \nu^{11} - 2450 \nu^{10} + 108 \nu^{9} + 15640 \nu^{8} - 7004 \nu^{7} - 46019 \nu^{6} + 25206 \nu^{5} + 63135 \nu^{4} - 30667 \nu^{3} - 37648 \nu^{2} + 10560 \nu + 8496 \)\()/368\)
\(\beta_{6}\)\(=\)\((\)\( 11 \nu^{13} - 47 \nu^{12} - 156 \nu^{11} + 808 \nu^{10} + 686 \nu^{9} - 5152 \nu^{8} - 664 \nu^{7} + 15225 \nu^{6} - 1989 \nu^{5} - 21091 \nu^{4} + 3544 \nu^{3} + 12241 \nu^{2} - 800 \nu - 2124 \)\()/92\)
\(\beta_{7}\)\(=\)\((\)\( -14 \nu^{13} - 5 \nu^{12} + 278 \nu^{11} + 130 \nu^{10} - 2090 \nu^{9} - 1196 \nu^{8} + 7444 \nu^{7} + 4986 \nu^{6} - 12843 \nu^{5} - 9660 \nu^{4} + 9877 \nu^{3} + 7661 \nu^{2} - 2620 \nu - 1604 \)\()/92\)
\(\beta_{8}\)\(=\)\((\)\( 49 \nu^{13} - 86 \nu^{12} - 858 \nu^{11} + 1362 \nu^{10} + 5636 \nu^{9} - 7728 \nu^{8} - 17452 \nu^{7} + 19119 \nu^{6} + 25826 \nu^{5} - 19251 \nu^{4} - 16273 \nu^{3} + 5168 \nu^{2} + 3144 \nu + 48 \)\()/184\)
\(\beta_{9}\)\(=\)\((\)\( 97 \nu^{13} - 266 \nu^{12} - 1522 \nu^{11} + 4386 \nu^{10} + 8412 \nu^{9} - 26680 \nu^{8} - 19396 \nu^{7} + 74967 \nu^{6} + 15014 \nu^{5} - 97451 \nu^{4} + 2763 \nu^{3} + 49860 \nu^{2} - 3040 \nu - 6544 \)\()/368\)
\(\beta_{10}\)\(=\)\((\)\( 10 \nu^{13} - 26 \nu^{12} - 169 \nu^{11} + 446 \nu^{10} + 1046 \nu^{9} - 2852 \nu^{8} - 2912 \nu^{7} + 8530 \nu^{6} + 3486 \nu^{5} - 12121 \nu^{4} - 1282 \nu^{3} + 7283 \nu^{2} - 31 \nu - 1266 \)\()/46\)
\(\beta_{11}\)\(=\)\((\)\( 12 \nu^{13} - 22 \nu^{12} - 212 \nu^{11} + 365 \nu^{10} + 1407 \nu^{9} - 2231 \nu^{8} - 4419 \nu^{7} + 6257 \nu^{6} + 6727 \nu^{5} - 8027 \nu^{4} - 4510 \nu^{3} + 4020 \nu^{2} + 961 \nu - 544 \)\()/46\)
\(\beta_{12}\)\(=\)\((\)\( 157 \nu^{13} - 146 \nu^{12} - 2858 \nu^{11} + 2002 \nu^{10} + 19748 \nu^{9} - 8832 \nu^{8} - 65388 \nu^{7} + 12435 \nu^{6} + 106310 \nu^{5} + 4761 \nu^{4} - 77057 \nu^{3} - 17164 \nu^{2} + 18072 \nu + 5088 \)\()/368\)
\(\beta_{13}\)\(=\)\((\)\( -177 \nu^{13} + 198 \nu^{12} + 3242 \nu^{11} - 2986 \nu^{10} - 22484 \nu^{9} + 15640 \nu^{8} + 74340 \nu^{7} - 33175 \nu^{6} - 119906 \nu^{5} + 21091 \nu^{4} + 85233 \nu^{3} + 8992 \nu^{2} - 18608 \nu - 6144 \)\()/368\)
\(1\)\(=\)\(\beta_0\)
\(\nu\)\(=\)\(\beta_{1}\)
\(\nu^{2}\)\(=\)\(\beta_{2} + 3\)
\(\nu^{3}\)\(=\)\(\beta_{4} + \beta_{3} + 5 \beta_{1} + 1\)
\(\nu^{4}\)\(=\)\(\beta_{6} + \beta_{5} + \beta_{4} + 7 \beta_{2} + \beta_{1} + 14\)
\(\nu^{5}\)\(=\)\(\beta_{13} + \beta_{8} - \beta_{7} + \beta_{6} + \beta_{5} + 9 \beta_{4} + 9 \beta_{3} + 30 \beta_{1} + 8\)
\(\nu^{6}\)\(=\)\(\beta_{13} + \beta_{12} + \beta_{11} - \beta_{9} + 11 \beta_{6} + 10 \beta_{5} + 11 \beta_{4} + 45 \beta_{2} + 12 \beta_{1} + 78\)
\(\nu^{7}\)\(=\)\(14 \beta_{13} + \beta_{12} + 3 \beta_{11} - \beta_{9} + 13 \beta_{8} - 12 \beta_{7} + 13 \beta_{6} + 13 \beta_{5} + 70 \beta_{4} + 65 \beta_{3} + \beta_{2} + 194 \beta_{1} + 58\)
\(\nu^{8}\)\(=\)\(16 \beta_{13} + 13 \beta_{12} + 17 \beta_{11} - 2 \beta_{10} - 14 \beta_{9} + 3 \beta_{8} - 2 \beta_{7} + 94 \beta_{6} + 80 \beta_{5} + 96 \beta_{4} + \beta_{3} + 289 \beta_{2} + 112 \beta_{1} + 475\)
\(\nu^{9}\)\(=\)\(137 \beta_{13} + 16 \beta_{12} + 50 \beta_{11} - 4 \beta_{10} - 16 \beta_{9} + 120 \beta_{8} - 105 \beta_{7} + 124 \beta_{6} + 122 \beta_{5} + 520 \beta_{4} + 445 \beta_{3} + 17 \beta_{2} + 1299 \beta_{1} + 418\)
\(\nu^{10}\)\(=\)\(177 \beta_{13} + 121 \beta_{12} + 195 \beta_{11} - 34 \beta_{10} - 136 \beta_{9} + 51 \beta_{8} - 38 \beta_{7} + 736 \beta_{6} + 601 \beta_{5} + 777 \beta_{4} + 22 \beta_{3} + 1877 \beta_{2} + 953 \beta_{1} + 3043\)
\(\nu^{11}\)\(=\)\(1168 \beta_{13} + 174 \beta_{12} + 558 \beta_{11} - 74 \beta_{10} - 172 \beta_{9} + 970 \beta_{8} - 826 \beta_{7} + 1057 \beta_{6} + 1015 \beta_{5} + 3789 \beta_{4} + 3004 \beta_{3} + 204 \beta_{2} + 8860 \beta_{1} + 3035\)
\(\nu^{12}\)\(=\)\(1673 \beta_{13} + 998 \beta_{12} + 1878 \beta_{11} - 384 \beta_{10} - 1144 \beta_{9} + 575 \beta_{8} - 467 \beta_{7} + 5533 \beta_{6} + 4407 \beta_{5} + 6070 \beta_{4} + 306 \beta_{3} + 12339 \beta_{2} + 7743 \beta_{1} + 20110\)
\(\nu^{13}\)\(=\)\(9303 \beta_{13} + 1611 \beta_{12} + 5255 \beta_{11} - 880 \beta_{10} - 1573 \beta_{9} + 7354 \beta_{8} - 6212 \beta_{7} + 8528 \beta_{6} + 7981 \beta_{5} + 27353 \beta_{4} + 20239 \beta_{3} + 2122 \beta_{2} + 61084 \beta_{1} + 22213\)

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
−2.55124
−1.98240
−1.86019
−1.37642
−0.894954
−0.656871
−0.429717
0.630703
1.14192
1.35292
1.57408
2.05175
2.31598
2.68441
−2.55124 0 4.50880 1.64740 0 −2.91756 −6.40055 0 −4.20290
1.2 −1.98240 0 1.92989 0.252916 0 −1.21499 0.138982 0 −0.501379
1.3 −1.86019 0 1.46029 −0.608499 0 0.188796 1.00396 0 1.13192
1.4 −1.37642 0 −0.105481 1.48313 0 4.92788 2.89802 0 −2.04140
1.5 −0.894954 0 −1.19906 −0.474904 0 −1.99579 2.86301 0 0.425017
1.6 −0.656871 0 −1.56852 −3.35329 0 −2.47996 2.34406 0 2.20268
1.7 −0.429717 0 −1.81534 3.93237 0 0.264416 1.63952 0 −1.68981
1.8 0.630703 0 −1.60221 −2.56371 0 2.03354 −2.27193 0 −1.61694
1.9 1.14192 0 −0.696014 4.45694 0 −4.52974 −3.07864 0 5.08948
1.10 1.35292 0 −0.169600 0.738177 0 3.44152 −2.93530 0 0.998696
1.11 1.57408 0 0.477741 −0.564555 0 −3.58089 −2.39616 0 −0.888657
1.12 2.05175 0 2.20969 −3.75134 0 −2.35999 0.430233 0 −7.69683
1.13 2.31598 0 3.36376 2.86683 0 3.60131 3.15843 0 6.63952
1.14 2.68441 0 5.20606 −1.06146 0 1.62145 8.60637 0 −2.84940
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.14
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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6003))\):

\(T_{2}^{14} - \cdots\)
\(T_{5}^{14} - \cdots\)