Properties

Label 24.4.d.a
Level 24
Weight 4
Character orbit 24.d
Analytic conductor 1.416
Analytic rank 0
Dimension 6
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 24.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(1.41604584014\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.8248384.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{5}\cdot 3^{2} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\ldots,\beta_{5}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q\) \( + \beta_{3} q^{2} \) \( + \beta_{1} q^{3} \) \( + ( 3 - \beta_{5} ) q^{4} \) \( + ( 2 \beta_{1} - \beta_{2} - \beta_{3} - \beta_{4} ) q^{5} \) \( + ( -1 + \beta_{2} ) q^{6} \) \( + ( 6 - \beta_{2} - 3 \beta_{3} + 2 \beta_{4} + \beta_{5} ) q^{7} \) \( + ( -14 - 4 \beta_{1} + 4 \beta_{3} - \beta_{4} - \beta_{5} ) q^{8} \) \( -9 q^{9} \) \(+O(q^{10})\) \( q\) \( + \beta_{3} q^{2} \) \( + \beta_{1} q^{3} \) \( + ( 3 - \beta_{5} ) q^{4} \) \( + ( 2 \beta_{1} - \beta_{2} - \beta_{3} - \beta_{4} ) q^{5} \) \( + ( -1 + \beta_{2} ) q^{6} \) \( + ( 6 - \beta_{2} - 3 \beta_{3} + 2 \beta_{4} + \beta_{5} ) q^{7} \) \( + ( -14 - 4 \beta_{1} + 4 \beta_{3} - \beta_{4} - \beta_{5} ) q^{8} \) \( -9 q^{9} \) \( + ( 10 - 8 \beta_{1} + 2 \beta_{2} + 2 \beta_{4} + 2 \beta_{5} ) q^{10} \) \( + ( 4 \beta_{2} - 4 \beta_{3} + 4 \beta_{5} ) q^{11} \) \( + ( -3 + 4 \beta_{1} - 3 \beta_{4} ) q^{12} \) \( + ( -4 \beta_{1} - 4 \beta_{2} - 2 \beta_{4} - 2 \beta_{5} ) q^{13} \) \( + ( -16 + 8 \beta_{1} + 2 \beta_{3} + 6 \beta_{4} + 2 \beta_{5} ) q^{14} \) \( + ( -14 - \beta_{2} + 9 \beta_{3} + 3 \beta_{5} ) q^{15} \) \( + ( 14 - 8 \beta_{1} - 4 \beta_{2} - 12 \beta_{3} - 2 \beta_{4} - 4 \beta_{5} ) q^{16} \) \( + ( 14 + 4 \beta_{2} - 12 \beta_{3} - 4 \beta_{4} - 8 \beta_{5} ) q^{17} \) \( -9 \beta_{3} q^{18} \) \( + ( -4 \beta_{1} + 4 \beta_{2} + 12 \beta_{3} + 8 \beta_{4} - 4 \beta_{5} ) q^{19} \) \( + ( 6 + 24 \beta_{1} - 8 \beta_{2} + 8 \beta_{3} - 2 \beta_{4} ) q^{20} \) \( + ( 2 \beta_{1} - 3 \beta_{2} + 9 \beta_{3} + 3 \beta_{4} - 6 \beta_{5} ) q^{21} \) \( + ( 32 + 32 \beta_{1} - 8 \beta_{4} + 8 \beta_{5} ) q^{22} \) \( + ( 52 + 2 \beta_{2} + 6 \beta_{3} - 4 \beta_{4} - 2 \beta_{5} ) q^{23} \) \( + ( 32 - 12 \beta_{1} + 4 \beta_{2} - 3 \beta_{4} + 3 \beta_{5} ) q^{24} \) \( + ( -39 + 48 \beta_{3} - 8 \beta_{4} + 8 \beta_{5} ) q^{25} \) \( + ( 12 - 32 \beta_{1} - 4 \beta_{2} + 8 \beta_{4} ) q^{26} \) \( -9 \beta_{1} q^{27} \) \( + ( -46 + 32 \beta_{1} + 8 \beta_{2} - 24 \beta_{3} + 8 \beta_{4} - 6 \beta_{5} ) q^{28} \) \( + ( -22 \beta_{1} + 7 \beta_{2} - \beta_{3} + 3 \beta_{4} + 4 \beta_{5} ) q^{29} \) \( + ( 72 + 8 \beta_{1} - 18 \beta_{3} + 6 \beta_{4} - 6 \beta_{5} ) q^{30} \) \( + ( -86 + \beta_{2} - 45 \beta_{3} + 6 \beta_{4} - 9 \beta_{5} ) q^{31} \) \( + ( -48 - 40 \beta_{1} - 8 \beta_{2} + 16 \beta_{3} + 6 \beta_{4} + 10 \beta_{5} ) q^{32} \) \( + ( 16 - 4 \beta_{2} - 36 \beta_{3} + 12 \beta_{4} ) q^{33} \) \( + ( -112 - 32 \beta_{1} + 30 \beta_{3} - 24 \beta_{4} + 8 \beta_{5} ) q^{34} \) \( + ( 4 \beta_{1} - 12 \beta_{2} - 20 \beta_{3} - 16 \beta_{4} + 4 \beta_{5} ) q^{35} \) \( + ( -27 + 9 \beta_{5} ) q^{36} \) \( + ( 40 \beta_{1} + 14 \beta_{2} - 30 \beta_{3} - 8 \beta_{4} + 22 \beta_{5} ) q^{37} \) \( + ( -124 + 32 \beta_{1} - 4 \beta_{2} - 8 \beta_{4} - 24 \beta_{5} ) q^{38} \) \( + ( 36 + 36 \beta_{3} - 6 \beta_{4} + 6 \beta_{5} ) q^{39} \) \( + ( 48 - 40 \beta_{1} + 24 \beta_{2} + 22 \beta_{4} - 6 \beta_{5} ) q^{40} \) \( + ( 66 - 12 \beta_{2} - 60 \beta_{3} + 28 \beta_{4} + 8 \beta_{5} ) q^{41} \) \( + ( -86 - 24 \beta_{1} + 2 \beta_{2} + 6 \beta_{4} - 18 \beta_{5} ) q^{42} \) \( + ( 36 \beta_{1} - 28 \beta_{2} + 12 \beta_{3} - 8 \beta_{4} - 20 \beta_{5} ) q^{43} \) \( + ( 176 + 32 \beta_{2} + 32 \beta_{3} + 16 \beta_{5} ) q^{44} \) \( + ( -18 \beta_{1} + 9 \beta_{2} + 9 \beta_{3} + 9 \beta_{4} ) q^{45} \) \( + ( 32 - 16 \beta_{1} + 60 \beta_{3} - 12 \beta_{4} - 4 \beta_{5} ) q^{46} \) \( + ( -92 + 2 \beta_{2} + 54 \beta_{3} - 12 \beta_{4} + 6 \beta_{5} ) q^{47} \) \( + ( 78 + 16 \beta_{1} - 12 \beta_{2} + 36 \beta_{3} - 12 \beta_{4} + 6 \beta_{5} ) q^{48} \) \( + ( 77 - 8 \beta_{2} + 72 \beta_{3} + 24 \beta_{5} ) q^{49} \) \( + ( 352 - 39 \beta_{3} - 32 \beta_{5} ) q^{50} \) \( + ( 30 \beta_{1} - 12 \beta_{2} - 36 \beta_{3} - 24 \beta_{4} + 12 \beta_{5} ) q^{51} \) \( + ( -52 + 16 \beta_{1} - 32 \beta_{2} + 20 \beta_{4} - 8 \beta_{5} ) q^{52} \) \( + ( 102 \beta_{1} + \beta_{2} + 41 \beta_{3} + 21 \beta_{4} - 20 \beta_{5} ) q^{53} \) \( + ( 9 - 9 \beta_{2} ) q^{54} \) \( + ( 224 + 8 \beta_{2} - 120 \beta_{3} + 8 \beta_{4} - 32 \beta_{5} ) q^{55} \) \( + ( -308 + 40 \beta_{1} + 32 \beta_{2} - 40 \beta_{3} - 22 \beta_{4} + 10 \beta_{5} ) q^{56} \) \( + ( -12 + 12 \beta_{2} - 36 \beta_{3} - 12 \beta_{4} - 24 \beta_{5} ) q^{57} \) \( + ( 18 + 56 \beta_{1} - 22 \beta_{2} - 14 \beta_{4} + 2 \beta_{5} ) q^{58} \) \( + ( -36 \beta_{1} + 32 \beta_{3} + 16 \beta_{4} - 16 \beta_{5} ) q^{59} \) \( + ( -218 + 8 \beta_{2} + 72 \beta_{3} + 6 \beta_{5} ) q^{60} \) \( + ( -160 \beta_{1} + 6 \beta_{2} - 30 \beta_{3} - 12 \beta_{4} + 18 \beta_{5} ) q^{61} \) \( + ( -336 - 8 \beta_{1} - 82 \beta_{3} - 6 \beta_{4} + 30 \beta_{5} ) q^{62} \) \( + ( -54 + 9 \beta_{2} + 27 \beta_{3} - 18 \beta_{4} - 9 \beta_{5} ) q^{63} \) \( + ( 180 + 32 \beta_{1} - 40 \beta_{2} - 72 \beta_{3} + 40 \beta_{4} - 12 \beta_{5} ) q^{64} \) \( + ( -328 + 4 \beta_{2} + 84 \beta_{3} - 20 \beta_{4} + 8 \beta_{5} ) q^{65} \) \( + ( -240 + 32 \beta_{1} + 24 \beta_{4} + 24 \beta_{5} ) q^{66} \) \( + ( -116 \beta_{1} + 48 \beta_{2} + 48 \beta_{3} + 48 \beta_{4} ) q^{67} \) \( + ( 522 - 64 \beta_{1} - 32 \beta_{2} - 96 \beta_{3} - 16 \beta_{4} + 2 \beta_{5} ) q^{68} \) \( + ( 60 \beta_{1} + 6 \beta_{2} - 18 \beta_{3} - 6 \beta_{4} + 12 \beta_{5} ) q^{69} \) \( + ( 220 - 96 \beta_{1} + 4 \beta_{2} + 24 \beta_{4} + 40 \beta_{5} ) q^{70} \) \( + ( -324 - 18 \beta_{2} + 90 \beta_{3} + 12 \beta_{4} + 42 \beta_{5} ) q^{71} \) \( + ( 126 + 36 \beta_{1} - 36 \beta_{3} + 9 \beta_{4} + 9 \beta_{5} ) q^{72} \) \( + ( 170 + 24 \beta_{2} - 24 \beta_{3} - 32 \beta_{4} - 40 \beta_{5} ) q^{73} \) \( + ( 232 + 112 \beta_{1} + 40 \beta_{2} - 28 \beta_{4} + 60 \beta_{5} ) q^{74} \) \( + ( -39 \beta_{1} + 48 \beta_{2} + 24 \beta_{4} + 24 \beta_{5} ) q^{75} \) \( + ( -260 - 144 \beta_{1} + 32 \beta_{2} - 96 \beta_{3} - 20 \beta_{4} - 16 \beta_{5} ) q^{76} \) \( + ( -256 \beta_{1} - 40 \beta_{2} + 40 \beta_{3} - 40 \beta_{5} ) q^{77} \) \( + ( 264 + 36 \beta_{3} - 24 \beta_{5} ) q^{78} \) \( + ( -14 - 11 \beta_{2} + 15 \beta_{3} + 14 \beta_{4} + 19 \beta_{5} ) q^{79} \) \( + ( -380 + 160 \beta_{1} - 40 \beta_{2} + 56 \beta_{3} - 56 \beta_{4} - 28 \beta_{5} ) q^{80} \) \( + 81 q^{81} \) \( + ( -368 + 96 \beta_{1} + 18 \beta_{3} + 72 \beta_{4} + 40 \beta_{5} ) q^{82} \) \( + ( 112 \beta_{1} + 12 \beta_{2} + 20 \beta_{3} + 16 \beta_{4} - 4 \beta_{5} ) q^{83} \) \( + ( -306 - 40 \beta_{1} - 24 \beta_{2} - 72 \beta_{3} - 18 \beta_{4} - 24 \beta_{5} ) q^{84} \) \( + ( 316 \beta_{1} - 70 \beta_{2} + 42 \beta_{3} - 14 \beta_{4} - 56 \beta_{5} ) q^{85} \) \( + ( -100 - 224 \beta_{1} + 36 \beta_{2} + 56 \beta_{4} - 24 \beta_{5} ) q^{86} \) \( + ( 202 - \beta_{2} - 63 \beta_{3} + 12 \beta_{4} - 9 \beta_{5} ) q^{87} \) \( + ( 224 + 192 \beta_{1} + 192 \beta_{3} - 80 \beta_{4} - 16 \beta_{5} ) q^{88} \) \( + ( -26 + 8 \beta_{2} - 24 \beta_{3} - 8 \beta_{4} - 16 \beta_{5} ) q^{89} \) \( + ( -90 + 72 \beta_{1} - 18 \beta_{2} - 18 \beta_{4} - 18 \beta_{5} ) q^{90} \) \( + ( 120 \beta_{1} + 20 \beta_{2} - 132 \beta_{3} - 56 \beta_{4} + 76 \beta_{5} ) q^{91} \) \( + ( 284 - 64 \beta_{1} - 16 \beta_{2} + 48 \beta_{3} - 16 \beta_{4} - 52 \beta_{5} ) q^{92} \) \( + ( -82 \beta_{1} - 45 \beta_{2} - 9 \beta_{3} - 27 \beta_{4} - 18 \beta_{5} ) q^{93} \) \( + ( 384 - 16 \beta_{1} - 84 \beta_{3} - 12 \beta_{4} - 36 \beta_{5} ) q^{94} \) \( + ( 920 - 20 \beta_{2} - 156 \beta_{3} + 56 \beta_{4} + 4 \beta_{5} ) q^{95} \) \( + ( 356 - 72 \beta_{1} + 16 \beta_{2} + 72 \beta_{3} + 30 \beta_{4} - 18 \beta_{5} ) q^{96} \) \( + ( -354 + 8 \beta_{2} - 120 \beta_{3} + 8 \beta_{4} - 32 \beta_{5} ) q^{97} \) \( + ( 576 + 64 \beta_{1} + 45 \beta_{3} + 48 \beta_{4} - 48 \beta_{5} ) q^{98} \) \( + ( -36 \beta_{2} + 36 \beta_{3} - 36 \beta_{5} ) q^{99} \) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(6q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 28q^{7} \) \(\mathstrut -\mathstrut 76q^{8} \) \(\mathstrut -\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut +\mathstrut 28q^{7} \) \(\mathstrut -\mathstrut 76q^{8} \) \(\mathstrut -\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut 60q^{10} \) \(\mathstrut -\mathstrut 12q^{12} \) \(\mathstrut -\mathstrut 100q^{14} \) \(\mathstrut -\mathstrut 60q^{15} \) \(\mathstrut +\mathstrut 56q^{16} \) \(\mathstrut +\mathstrut 52q^{17} \) \(\mathstrut -\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut 224q^{22} \) \(\mathstrut +\mathstrut 328q^{23} \) \(\mathstrut +\mathstrut 204q^{24} \) \(\mathstrut -\mathstrut 106q^{25} \) \(\mathstrut +\mathstrut 56q^{26} \) \(\mathstrut -\mathstrut 352q^{28} \) \(\mathstrut +\mathstrut 372q^{30} \) \(\mathstrut -\mathstrut 636q^{31} \) \(\mathstrut -\mathstrut 248q^{32} \) \(\mathstrut -\mathstrut 548q^{34} \) \(\mathstrut -\mathstrut 144q^{36} \) \(\mathstrut -\mathstrut 776q^{38} \) \(\mathstrut +\mathstrut 312q^{39} \) \(\mathstrut +\mathstrut 232q^{40} \) \(\mathstrut +\mathstrut 236q^{41} \) \(\mathstrut -\mathstrut 564q^{42} \) \(\mathstrut +\mathstrut 1152q^{44} \) \(\mathstrut +\mathstrut 328q^{46} \) \(\mathstrut -\mathstrut 408q^{47} \) \(\mathstrut +\mathstrut 576q^{48} \) \(\mathstrut +\mathstrut 654q^{49} \) \(\mathstrut +\mathstrut 1970q^{50} \) \(\mathstrut -\mathstrut 368q^{52} \) \(\mathstrut +\mathstrut 54q^{54} \) \(\mathstrut +\mathstrut 1024q^{55} \) \(\mathstrut -\mathstrut 1864q^{56} \) \(\mathstrut -\mathstrut 168q^{57} \) \(\mathstrut +\mathstrut 140q^{58} \) \(\mathstrut -\mathstrut 1152q^{60} \) \(\mathstrut -\mathstrut 2108q^{62} \) \(\mathstrut -\mathstrut 252q^{63} \) \(\mathstrut +\mathstrut 832q^{64} \) \(\mathstrut -\mathstrut 1744q^{65} \) \(\mathstrut -\mathstrut 1440q^{66} \) \(\mathstrut +\mathstrut 2976q^{68} \) \(\mathstrut +\mathstrut 1352q^{70} \) \(\mathstrut -\mathstrut 1704q^{71} \) \(\mathstrut +\mathstrut 684q^{72} \) \(\mathstrut +\mathstrut 956q^{73} \) \(\mathstrut +\mathstrut 1568q^{74} \) \(\mathstrut -\mathstrut 1744q^{76} \) \(\mathstrut +\mathstrut 1608q^{78} \) \(\mathstrut -\mathstrut 44q^{79} \) \(\mathstrut -\mathstrut 2112q^{80} \) \(\mathstrut +\mathstrut 486q^{81} \) \(\mathstrut -\mathstrut 2236q^{82} \) \(\mathstrut -\mathstrut 1992q^{84} \) \(\mathstrut -\mathstrut 760q^{86} \) \(\mathstrut +\mathstrut 1044q^{87} \) \(\mathstrut +\mathstrut 1856q^{88} \) \(\mathstrut -\mathstrut 220q^{89} \) \(\mathstrut -\mathstrut 540q^{90} \) \(\mathstrut +\mathstrut 1728q^{92} \) \(\mathstrut +\mathstrut 2088q^{94} \) \(\mathstrut +\mathstrut 5104q^{95} \) \(\mathstrut +\mathstrut 2184q^{96} \) \(\mathstrut -\mathstrut 2444q^{97} \) \(\mathstrut +\mathstrut 3354q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Basis of coefficient ring in terms of a root \(\nu\) of \(x^{6}\mathstrut +\mathstrut \) \(x^{4}\mathstrut -\mathstrut \) \(12\) \(x^{3}\mathstrut +\mathstrut \) \(4\) \(x^{2}\mathstrut +\mathstrut \) \(64\):

\(\beta_{0}\)\(=\)\( 1 \)
\(\beta_{1}\)\(=\)\((\)\( -3 \nu^{5} - 6 \nu^{4} + 9 \nu^{3} + 6 \nu^{2} + 24 \nu - 96 \)\()/32\)
\(\beta_{2}\)\(=\)\((\)\( -3 \nu^{4} - 6 \nu^{3} + 9 \nu^{2} + 6 \nu + 32 \)\()/8\)
\(\beta_{3}\)\(=\)\((\)\( -\nu^{5} + \nu^{4} + \nu^{3} + 9 \nu^{2} - 6 \nu - 8 \)\()/8\)
\(\beta_{4}\)\(=\)\((\)\( -\nu^{5} + 2 \nu^{4} + 3 \nu^{3} + 6 \nu^{2} - 40 \nu - 24 \)\()/8\)
\(\beta_{5}\)\(=\)\((\)\( -\nu^{5} + 4 \nu^{4} - 9 \nu^{3} - 28 \nu + 56 \)\()/8\)
\(1\)\(=\)\(\beta_0\)
\(\nu\)\(=\)\((\)\(-\)\(3\) \(\beta_{4}\mathstrut +\mathstrut \) \(3\) \(\beta_{3}\mathstrut -\mathstrut \) \(\beta_{2}\mathstrut -\mathstrut \) \(2\)\()/12\)
\(\nu^{2}\)\(=\)\((\)\(-\)\(3\) \(\beta_{5}\mathstrut +\mathstrut \) \(9\) \(\beta_{3}\mathstrut +\mathstrut \) \(3\) \(\beta_{2}\mathstrut -\mathstrut \) \(8\) \(\beta_{1}\mathstrut -\mathstrut \) \(6\)\()/12\)
\(\nu^{3}\)\(=\)\((\)\(-\)\(6\) \(\beta_{5}\mathstrut +\mathstrut \) \(3\) \(\beta_{4}\mathstrut +\mathstrut \) \(3\) \(\beta_{3}\mathstrut -\mathstrut \) \(5\) \(\beta_{2}\mathstrut +\mathstrut \) \(74\)\()/12\)
\(\nu^{4}\)\(=\)\((\)\(\beta_{5}\mathstrut -\mathstrut \) \(4\) \(\beta_{4}\mathstrut +\mathstrut \) \(9\) \(\beta_{3}\mathstrut -\mathstrut \) \(5\) \(\beta_{2}\mathstrut -\mathstrut \) \(8\) \(\beta_{1}\mathstrut -\mathstrut \) \(14\)\()/4\)
\(\nu^{5}\)\(=\)\((\)\(-\)\(30\) \(\beta_{5}\mathstrut +\mathstrut \) \(9\) \(\beta_{4}\mathstrut -\mathstrut \) \(3\) \(\beta_{3}\mathstrut +\mathstrut \) \(13\) \(\beta_{2}\mathstrut -\mathstrut \) \(96\) \(\beta_{1}\mathstrut -\mathstrut \) \(106\)\()/12\)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(13\) \(17\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
13.1
−1.24181 + 1.56777i
−1.24181 1.56777i
−0.641412 + 1.89436i
−0.641412 1.89436i
1.88322 0.673417i
1.88322 + 0.673417i
−2.80958 0.325969i 3.00000i 7.78749 + 1.83167i 18.5422i 0.977907 8.42874i 9.32669 −21.2825 7.68472i −9.00000 6.04419 52.0958i
13.2 −2.80958 + 0.325969i 3.00000i 7.78749 1.83167i 18.5422i 0.977907 + 8.42874i 9.32669 −21.2825 + 7.68472i −9.00000 6.04419 + 52.0958i
13.3 1.25295 2.53577i 3.00000i −4.86025 6.35436i 9.15486i −7.60731 3.75884i 27.4175 −22.2028 + 4.36281i −9.00000 23.2146 + 11.4705i
13.4 1.25295 + 2.53577i 3.00000i −4.86025 + 6.35436i 9.15486i −7.60731 + 3.75884i 27.4175 −22.2028 4.36281i −9.00000 23.2146 11.4705i
13.5 2.55664 1.20980i 3.00000i 5.07277 6.18604i 0.612661i 3.62940 + 7.66991i −22.7441 5.48534 21.9525i −9.00000 0.741198 + 1.56635i
13.6 2.55664 + 1.20980i 3.00000i 5.07277 + 6.18604i 0.612661i 3.62940 7.66991i −22.7441 5.48534 + 21.9525i −9.00000 0.741198 1.56635i
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 13.6
Significant digits:
Format:

Inner twists

Char. orbit Parity Mult. Self Twist Proved
1.a Even 1 trivial yes
8.b Even 1 yes

Hecke kernels

There are no other newforms in \(S_{4}^{\mathrm{new}}(24, [\chi])\).