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Properties

Label 25.10.d.a
Level $25$
Weight $10$
Character orbit 25.d
Analytic conductor $12.876$
Analytic rank $0$
Dimension $84$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [25,10,Mod(6,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.6");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 25.d (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(12.8758959041\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(21\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 84 q + 13 q^{2} - 151 q^{3} - 4867 q^{4} - 4610 q^{5} + 3613 q^{6} - 5952 q^{7} + 14380 q^{8} - 131668 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 84 q + 13 q^{2} - 151 q^{3} - 4867 q^{4} - 4610 q^{5} + 3613 q^{6} - 5952 q^{7} + 14380 q^{8} - 131668 q^{9} + 1245 q^{10} + 47263 q^{11} + 151723 q^{12} + 909 q^{13} + 447871 q^{14} + 503025 q^{15} - 1967951 q^{16} - 152947 q^{17} - 1616016 q^{18} - 153395 q^{19} + 2977895 q^{20} + 1363008 q^{21} + 3660856 q^{22} + 4511089 q^{23} - 6818340 q^{24} - 9025280 q^{25} - 9688002 q^{26} - 3093085 q^{27} + 14115291 q^{28} + 712235 q^{29} + 21469035 q^{30} + 12756873 q^{31} - 32632362 q^{32} - 17130997 q^{33} + 7156541 q^{34} - 3060310 q^{35} + 6272269 q^{36} + 1644153 q^{37} + 6940445 q^{38} + 19494259 q^{39} - 57859470 q^{40} + 58333433 q^{41} - 37033219 q^{42} + 18427044 q^{43} + 125934396 q^{44} + 19423100 q^{45} - 105780007 q^{46} + 2767903 q^{47} + 5333194 q^{48} + 255772608 q^{49} - 206520835 q^{50} - 201283402 q^{51} + 28038408 q^{52} + 2054259 q^{53} + 565992175 q^{54} + 156884185 q^{55} - 416924310 q^{56} - 394535090 q^{57} - 740737250 q^{58} - 277069545 q^{59} + 567102810 q^{60} + 577284343 q^{61} - 46901544 q^{62} - 521860846 q^{63} - 1004145332 q^{64} - 1073691795 q^{65} + 1231043336 q^{66} + 154291493 q^{67} + 2959898126 q^{68} + 697866359 q^{69} + 857155880 q^{70} + 283347593 q^{71} - 724050335 q^{72} - 408433491 q^{73} - 2573796684 q^{74} - 159946705 q^{75} - 2429050880 q^{76} + 1412345336 q^{77} - 633477007 q^{78} + 994068455 q^{79} + 3123251580 q^{80} - 1664568886 q^{81} + 2667623986 q^{82} - 236717391 q^{83} - 600996364 q^{84} - 4229780835 q^{85} + 1092217503 q^{86} - 5688376045 q^{87} - 19076640 q^{88} + 1250480095 q^{89} + 3227628655 q^{90} + 1492351208 q^{91} - 4800624792 q^{92} + 4719812398 q^{93} + 4097235701 q^{94} + 5674562545 q^{95} - 1118596442 q^{96} - 4675486937 q^{97} - 4419748384 q^{98} - 3960658276 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
6.1 −12.6660 − 38.9819i 25.3455 − 18.4146i −944.942 + 686.540i −343.622 − 1354.64i −1038.86 − 754.776i −5047.13 21753.3 + 15804.7i −5779.08 + 17786.2i −48454.1 + 30552.9i
6.2 −12.1436 − 37.3742i 74.5570 − 54.1688i −835.144 + 606.768i −388.149 + 1342.56i −2929.91 − 2128.70i 11814.9 16541.4 + 12018.0i −3457.90 + 10642.3i 54890.5 − 1796.78i
6.3 −11.9592 − 36.8066i −178.461 + 129.660i −797.484 + 579.406i −868.240 + 1095.12i 6906.58 + 5017.92i −9282.38 14832.7 + 10776.6i 8954.40 − 27558.8i 50691.0 + 18860.2i
6.4 −10.3447 − 31.8376i 163.209 − 118.578i −492.405 + 357.753i 1394.33 + 94.7632i −5463.59 − 3969.53i −5454.94 2617.42 + 1901.67i 6493.99 − 19986.4i −11406.8 − 45372.3i
6.5 −9.51544 − 29.2855i −143.715 + 104.415i −352.881 + 256.383i 1312.92 − 478.914i 4425.34 + 3215.20i 6177.17 −1888.69 − 1372.22i 3669.05 − 11292.2i −26518.3 − 33892.5i
6.6 −7.54216 − 23.2124i −26.7307 + 19.4210i −67.7135 + 49.1968i −1015.27 − 960.391i 652.415 + 474.007i 1491.56 −8457.08 − 6144.43i −5745.03 + 17681.4i −14635.6 + 30810.3i
6.7 −6.02773 − 18.5515i 178.921 − 129.994i 106.394 − 77.2996i −1395.56 + 74.3942i −3490.07 − 2535.68i −2427.08 −10155.1 − 7378.12i 9032.02 − 27797.7i 9792.19 + 25441.3i
6.8 −5.39139 − 16.5930i −17.9118 + 13.0137i 167.956 − 122.027i 759.372 + 1173.23i 312.505 + 227.048i −6139.01 −10157.1 − 7379.58i −5930.91 + 18253.4i 15373.4 − 18925.6i
6.9 −2.29120 − 7.05158i −97.9155 + 71.1397i 369.742 − 268.633i −1052.85 + 919.034i 725.991 + 527.463i 5123.37 −5812.63 − 4223.12i −1555.81 + 4788.29i 8892.94 + 5318.59i
6.10 −1.93400 − 5.95225i 115.282 − 83.7573i 382.528 − 277.923i 827.483 − 1126.23i −721.500 − 524.200i 5949.13 −4986.48 − 3622.89i 192.275 − 591.762i −8303.96 − 2747.25i
6.11 −1.14570 − 3.52611i −212.262 + 154.217i 403.096 − 292.866i −636.565 − 1244.15i 786.976 + 571.771i −3758.30 −3030.25 − 2201.60i 15189.7 − 46749.1i −3657.70 + 3670.03i
6.12 2.17861 + 6.70507i −35.8669 + 26.0588i 374.005 − 271.731i 896.991 − 1071.70i −252.866 − 183.718i −10285.3 5557.06 + 4037.44i −5475.01 + 16850.3i 9139.99 + 3679.58i
6.13 3.15659 + 9.71498i 146.440 − 106.395i 329.800 − 239.614i 171.642 + 1386.96i 1495.88 + 1086.82i 3081.13 7600.08 + 5521.78i 4042.48 − 12441.5i −12932.5 + 6045.56i
6.14 4.12283 + 12.6888i −143.634 + 104.356i 270.210 − 196.319i 1272.25 + 578.356i −1916.33 − 1392.29i 5409.74 9131.45 + 6634.39i 3658.09 − 11258.5i −2093.34 + 18527.8i
6.15 4.80600 + 14.7914i 50.2719 − 36.5246i 218.530 − 158.772i −1397.47 − 14.4261i 781.856 + 568.051i −9345.57 9840.83 + 7149.78i −4889.17 + 15047.3i −6502.85 − 20739.8i
6.16 7.07699 + 21.7807i −13.8652 + 10.0736i −10.1005 + 7.33845i −943.727 − 1030.78i −317.535 − 230.703i 11104.3 9254.92 + 6724.09i −5991.62 + 18440.3i 15772.4 − 27849.9i
6.17 9.34369 + 28.7569i 220.950 − 160.530i −325.439 + 236.445i −87.5993 − 1394.79i 6680.83 + 4853.91i −4225.18 2684.36 + 1950.30i 16966.8 − 52218.5i 39291.5 − 15551.6i
6.18 9.41477 + 28.9757i −153.497 + 111.522i −336.736 + 244.653i −694.459 + 1212.79i −4676.56 − 3397.72i −3948.26 2360.61 + 1715.08i 5041.74 − 15516.9i −41679.5 − 8704.31i
6.19 10.4128 + 32.0472i 60.4006 − 43.8836i −504.379 + 366.453i 1341.50 + 391.810i 2035.28 + 1478.72i −747.877 −3038.14 − 2207.34i −4359.92 + 13418.4i 1412.26 + 47071.0i
6.20 12.0886 + 37.2049i −132.635 + 96.3652i −823.853 + 598.564i 347.649 − 1353.61i −5188.63 − 3769.76i −1623.61 −16024.8 − 11642.7i 2223.49 − 6843.19i 54563.6 − 3429.04i
See all 84 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 6.21
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
25.d even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 25.10.d.a ✓ 84
25.d even 5 1 inner 25.10.d.a ✓ 84
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
25.10.d.a ✓ 84 1.a even 1 1 trivial
25.10.d.a ✓ 84 25.d even 5 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{10}^{\mathrm{new}}(25, [\chi])\).