Properties

Label 2.26.a
Level 2
Weight 26
Character orbit a
Rep. character \(\chi_{2}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 6
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 26 \)
Character orbit: \([\chi]\) = 2.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(2))\).

Total New Old
Modular forms 7 3 4
Cusp forms 5 3 2
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(2\)Dim.
\(+\)\(1\)
\(-\)\(2\)

Trace form

\(3q \) \(\mathstrut +\mathstrut 4096q^{2} \) \(\mathstrut +\mathstrut 477804q^{3} \) \(\mathstrut +\mathstrut 50331648q^{4} \) \(\mathstrut +\mathstrut 1082958450q^{5} \) \(\mathstrut +\mathstrut 1154629632q^{6} \) \(\mathstrut -\mathstrut 41259174312q^{7} \) \(\mathstrut +\mathstrut 68719476736q^{8} \) \(\mathstrut +\mathstrut 2456838201159q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 4096q^{2} \) \(\mathstrut +\mathstrut 477804q^{3} \) \(\mathstrut +\mathstrut 50331648q^{4} \) \(\mathstrut +\mathstrut 1082958450q^{5} \) \(\mathstrut +\mathstrut 1154629632q^{6} \) \(\mathstrut -\mathstrut 41259174312q^{7} \) \(\mathstrut +\mathstrut 68719476736q^{8} \) \(\mathstrut +\mathstrut 2456838201159q^{9} \) \(\mathstrut +\mathstrut 1642281984000q^{10} \) \(\mathstrut -\mathstrut 6183187766844q^{11} \) \(\mathstrut +\mathstrut 8016220913664q^{12} \) \(\mathstrut -\mathstrut 18623063615286q^{13} \) \(\mathstrut +\mathstrut 165912987336704q^{14} \) \(\mathstrut -\mathstrut 1418778892971000q^{15} \) \(\mathstrut +\mathstrut 844424930131968q^{16} \) \(\mathstrut -\mathstrut 1327546948772682q^{17} \) \(\mathstrut +\mathstrut 16925592224452608q^{18} \) \(\mathstrut -\mathstrut 14476503947047140q^{19} \) \(\mathstrut +\mathstrut 18169027834675200q^{20} \) \(\mathstrut -\mathstrut 98865491287772064q^{21} \) \(\mathstrut +\mathstrut 93508636620275712q^{22} \) \(\mathstrut -\mathstrut 29452245057438456q^{23} \) \(\mathstrut +\mathstrut 19371470736064512q^{24} \) \(\mathstrut +\mathstrut 13625643203968125q^{25} \) \(\mathstrut -\mathstrut 795898030855364608q^{26} \) \(\mathstrut +\mathstrut 2006515475993054520q^{27} \) \(\mathstrut -\mathstrut 692214079414075392q^{28} \) \(\mathstrut +\mathstrut 3804643074807962490q^{29} \) \(\mathstrut -\mathstrut 6084959981978419200q^{30} \) \(\mathstrut -\mathstrut 6024549917048451744q^{31} \) \(\mathstrut +\mathstrut 1152921504606846976q^{32} \) \(\mathstrut -\mathstrut 4777633723177011312q^{33} \) \(\mathstrut +\mathstrut 16315616415746433024q^{34} \) \(\mathstrut +\mathstrut 16630841714950218000q^{35} \) \(\mathstrut +\mathstrut 41218905177895993344q^{36} \) \(\mathstrut -\mathstrut 86287972030065606702q^{37} \) \(\mathstrut +\mathstrut 55387527008863600640q^{38} \) \(\mathstrut -\mathstrut 144889527996244146072q^{39} \) \(\mathstrut +\mathstrut 27552919578476544000q^{40} \) \(\mathstrut +\mathstrut 316574131640178799806q^{41} \) \(\mathstrut -\mathstrut 372146552978360107008q^{42} \) \(\mathstrut +\mathstrut 4406011488742288164q^{43} \) \(\mathstrut -\mathstrut 103736676732899426304q^{44} \) \(\mathstrut +\mathstrut 331401278747581619850q^{45} \) \(\mathstrut -\mathstrut 823942375446566043648q^{46} \) \(\mathstrut +\mathstrut 2149187127091682220048q^{47} \) \(\mathstrut +\mathstrut 134489869772258279424q^{48} \) \(\mathstrut -\mathstrut 524397224512548705429q^{49} \) \(\mathstrut +\mathstrut 1544613042178577920000q^{50} \) \(\mathstrut -\mathstrut 7254340889000213332584q^{51} \) \(\mathstrut -\mathstrut 312443160855394123776q^{52} \) \(\mathstrut -\mathstrut 2817100001721097140606q^{53} \) \(\mathstrut +\mathstrut 9570810422957059768320q^{54} \) \(\mathstrut -\mathstrut 259329155335977018600q^{55} \) \(\mathstrut +\mathstrut 2783558025753147736064q^{56} \) \(\mathstrut +\mathstrut 14809787410741003134960q^{57} \) \(\mathstrut -\mathstrut 1457429644882294087680q^{58} \) \(\mathstrut -\mathstrut 25752580702182118552620q^{59} \) \(\mathstrut -\mathstrut 23803159943615348736000q^{60} \) \(\mathstrut +\mathstrut 58273808422153400946906q^{61} \) \(\mathstrut -\mathstrut 46496213645941973843968q^{62} \) \(\mathstrut -\mathstrut 2378665557655847152776q^{63} \) \(\mathstrut +\mathstrut 14167099448608935641088q^{64} \) \(\mathstrut +\mathstrut 33639177305668163029500q^{65} \) \(\mathstrut -\mathstrut 7928589045076086030336q^{66} \) \(\mathstrut -\mathstrut 91687165138132830937812q^{67} \) \(\mathstrut -\mathstrut 22272541909700220813312q^{68} \) \(\mathstrut +\mathstrut 133545663071151999943968q^{69} \) \(\mathstrut +\mathstrut 182326222209622243737600q^{70} \) \(\mathstrut -\mathstrut 371396990842508553600744q^{71} \) \(\mathstrut +\mathstrut 283964316677561886179328q^{72} \) \(\mathstrut +\mathstrut 353864430262753766920734q^{73} \) \(\mathstrut +\mathstrut 67466215139595328446464q^{74} \) \(\mathstrut -\mathstrut 1162701372097460046907500q^{75} \) \(\mathstrut -\mathstrut 242875433644462429962240q^{76} \) \(\mathstrut +\mathstrut 686668981303319284175136q^{77} \) \(\mathstrut -\mathstrut 663958403786416396468224q^{78} \) \(\mathstrut +\mathstrut 123276068749625658422640q^{79} \) \(\mathstrut +\mathstrut 304825704492358120243200q^{80} \) \(\mathstrut +\mathstrut 2602795698165838861769643q^{81} \) \(\mathstrut -\mathstrut 616634298074201546907648q^{82} \) \(\mathstrut -\mathstrut 443559281547277297098276q^{83} \) \(\mathstrut -\mathstrut 1658687702281070076493824q^{84} \) \(\mathstrut +\mathstrut 1934938263012912585418500q^{85} \) \(\mathstrut +\mathstrut 346821450457913407619072q^{86} \) \(\mathstrut -\mathstrut 6460593803049848600508120q^{87} \) \(\mathstrut +\mathstrut 1568814594443875599777792q^{88} \) \(\mathstrut +\mathstrut 1209100457235696633777870q^{89} \) \(\mathstrut +\mathstrut 3697528938303212522496000q^{90} \) \(\mathstrut -\mathstrut 1001998704753591930702384q^{91} \) \(\mathstrut -\mathstrut 494126677013577383018496q^{92} \) \(\mathstrut -\mathstrut 1627354974425964978364032q^{93} \) \(\mathstrut +\mathstrut 6510732644424363948048384q^{94} \) \(\mathstrut -\mathstrut 10222902461728178016279000q^{95} \) \(\mathstrut +\mathstrut 324999348776633307758592q^{96} \) \(\mathstrut +\mathstrut 4984992770493732599418918q^{97} \) \(\mathstrut -\mathstrut 4853924091950689643163648q^{98} \) \(\mathstrut +\mathstrut 23986549987983068504983668q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(2))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
2.26.a.a \(1\) \(7.920\) \(\Q\) None \(-4096\) \(97956\) \(341005350\) \(-40882637368\) \(+\) \(q-2^{12}q^{2}+97956q^{3}+2^{24}q^{4}+341005350q^{5}+\cdots\)
2.26.a.b \(2\) \(7.920\) \(\Q(\sqrt{106705}) \) None \(8192\) \(379848\) \(741953100\) \(-376536944\) \(-\) \(q+2^{12}q^{2}+(189924-\beta )q^{3}+2^{24}q^{4}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)