Properties

Label 2.26
Level 2
Weight 26
Dimension 3
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 26 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(2))\).

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

Trace form

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

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(2))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2.26.a \(\chi_{2}(1, \cdot)\) 2.26.a.a 1 1
2.26.a.b 2

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)