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Properties

Label 25.16.e
Level $25$
Weight $16$
Character orbit 25.e
Rep. character $\chi_{25}(4,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $144$
Sturm bound $40$

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 16 \)
Character orbit: \([\chi]\) \(=\) 25.e (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(40\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(25, [\chi])\).

Total New Old
Modular forms 152 152 0
Cusp forms 144 144 0
Eisenstein series 8 8 0

Trace form

\( 144 q - 5 q^{2} - 5 q^{3} + 557053 q^{4} + 220365 q^{5} + 494333 q^{6} + 28408690 q^{8} + 163382717 q^{9} + O(q^{10}) \) \( 144 q - 5 q^{2} - 5 q^{3} + 557053 q^{4} + 220365 q^{5} + 494333 q^{6} + 28408690 q^{8} + 163382717 q^{9} + 48274195 q^{10} - 8455357 q^{11} + 235274235 q^{12} - 5 q^{13} - 404794289 q^{14} + 2227350375 q^{15} - 4902872791 q^{16} - 3405942565 q^{17} - 9898335475 q^{19} + 30428396595 q^{20} - 2016834822 q^{21} - 62054060370 q^{22} - 73709670325 q^{23} + 125502608080 q^{24} - 62695986155 q^{25} - 144457843182 q^{26} - 70583658605 q^{27} + 395332321275 q^{28} - 34252132655 q^{29} - 116970737765 q^{30} + 502236696513 q^{31} + 128974309115 q^{33} - 1706285297939 q^{34} - 508487807610 q^{35} - 5107098560931 q^{36} + 1951366884140 q^{37} - 8189168307345 q^{38} - 2009590519241 q^{39} + 5086630821530 q^{40} + 2077894592183 q^{41} - 9268986157555 q^{42} - 567439082324 q^{44} + 679331957775 q^{45} + 1699067625153 q^{46} + 6806533079505 q^{47} + 27552161184810 q^{48} - 84948219817132 q^{49} - 9242807513835 q^{50} - 13914843508182 q^{51} - 61975112197260 q^{52} - 58858823969170 q^{53} + 11607223856705 q^{54} + 22526044827885 q^{55} + 48546421847920 q^{56} - 168976909125630 q^{58} - 43676057270385 q^{59} + 94124175892760 q^{60} - 21947186769147 q^{61} + 118867689917520 q^{62} + 51233175930450 q^{63} + 80074140819948 q^{64} - 116606305202320 q^{65} - 5704942890254 q^{66} - 189011385420605 q^{67} + 56297064763979 q^{69} - 258855282302970 q^{70} + 461232527545113 q^{71} + 538167454461215 q^{72} + 559503038658355 q^{73} + 1028477989168836 q^{74} + 196959969182045 q^{75} - 1302293669337280 q^{76} - 873706061828930 q^{77} - 57280105972505 q^{78} + 153755706697735 q^{79} + 2837525942966930 q^{80} + 170960736857919 q^{81} - 1220101853960625 q^{83} - 915229442645934 q^{84} + 1061816455788490 q^{85} + 669475293397803 q^{86} - 183144353895085 q^{87} + 720515957797950 q^{88} + 168707237889800 q^{89} + 678621472550255 q^{90} + 946199445216098 q^{91} + 7678650758679690 q^{92} - 3134456404338599 q^{94} - 5502927996187455 q^{95} - 3114496320825472 q^{96} + 1067628787316185 q^{97} + 7973969687452580 q^{98} + 3914241450223224 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.