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Properties

Label 49.26.c
Level $49$
Weight $26$
Character orbit 49.c
Rep. character $\chi_{49}(18,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $162$
Sturm bound $121$

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Defining parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 49.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(121\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(49, [\chi])\).

Total New Old
Modular forms 242 170 72
Cusp forms 226 162 64
Eisenstein series 16 8 8

Trace form

\( 162 q + 8099 q^{2} - 531440 q^{3} - 1272902569 q^{4} - 288173088 q^{5} + 13063290884 q^{6} - 660252181146 q^{8} - 20266472294605 q^{9} + O(q^{10}) \) \( 162 q + 8099 q^{2} - 531440 q^{3} - 1272902569 q^{4} - 288173088 q^{5} + 13063290884 q^{6} - 660252181146 q^{8} - 20266472294605 q^{9} + 918803280822 q^{10} + 2016528183068 q^{11} - 59498382182260 q^{12} - 136259290951840 q^{13} + 4027505659964992 q^{15} - 17424498018519013 q^{16} - 5022112861130400 q^{17} - 1260539526059207 q^{18} - 10588631642557696 q^{19} - 24731206489166184 q^{20} + 335790345452902748 q^{22} - 11355073287516728 q^{23} - 573793671932159616 q^{24} - 3968380940427789339 q^{25} - 2724774668939531124 q^{26} + 2206109587432690240 q^{27} + 12342571135330945252 q^{29} + 7147958054062539438 q^{30} - 10841379318391039264 q^{31} - 9338437340063962475 q^{32} + 11546953084647657040 q^{33} - 13082632789597647612 q^{34} + 379671809825708755706 q^{36} - 122696581688775691114 q^{37} + 70525127026788123690 q^{38} + 219454727497317240656 q^{39} + 85110519871079993136 q^{40} + 330540029228046240288 q^{41} + 349272240470524755176 q^{43} + 1163696416021133251204 q^{44} - 485170985786336771600 q^{45} - 2196717861285308543282 q^{46} - 2014371898465936816800 q^{47} + 11662563919658426657120 q^{48} + 10766101679656698973922 q^{50} + 11366969051125707331456 q^{51} - 6992249387859106251160 q^{52} - 3298975314994960189190 q^{53} - 34981309708344282421726 q^{54} + 65886425153156913843552 q^{55} - 59258800160658873823200 q^{57} - 3404712189216416236802 q^{58} + 10935316261765587024144 q^{59} - 195838364083254425358028 q^{60} + 17484129051186787701488 q^{61} + 262788504919801688816100 q^{62} + 182607523445129741148186 q^{64} + 254078107829348375161008 q^{65} - 61498292814044614748374 q^{66} - 127639865134885885527284 q^{67} - 482184105822238591781100 q^{68} + 815717958910888805206848 q^{69} + 898852441428296398668704 q^{71} + 623322930837426782957421 q^{72} - 181923789786333620742640 q^{73} + 262138346407180592837052 q^{74} + 66014699727433523602592 q^{75} - 1262772869625204941438344 q^{76} + 413573597068840224576840 q^{78} - 1061245299373646398551288 q^{79} + 1229118480867135510718416 q^{80} - 4831347628603930870848553 q^{81} + 4913051673767471255932260 q^{82} - 4355401847600512595234880 q^{83} - 2058199104688161494171040 q^{85} - 5285101820154356756981040 q^{86} + 2195492958449506107537040 q^{87} + 7044581474010084680667192 q^{88} - 449697822243925695740496 q^{89} - 41750741714541116033274904 q^{90} - 6563761222030039333716856 q^{92} - 8053034653241927776563440 q^{93} + 1689612490320614160295890 q^{94} + 5843912046525400627182384 q^{95} + 3851732620967552391601888 q^{96} + 17074074602311685528685920 q^{97} + 62773827605290581254201288 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{26}^{\mathrm{new}}(49, [\chi])\) into newform subspaces

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

Decomposition of \(S_{26}^{\mathrm{old}}(49, [\chi])\) into lower level spaces

\( S_{26}^{\mathrm{old}}(49, [\chi]) \cong \) \(S_{26}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)