Properties

Label 49.26.g
Level $49$
Weight $26$
Character orbit 49.g
Rep. character $\chi_{49}(2,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1392$
Sturm bound $121$

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Defining parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 26 \)
Character orbit: \([\chi]\) \(=\) 49.g (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(121\)

Dimensions

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

Total New Old
Modular forms 1416 1416 0
Cusp forms 1392 1392 0
Eisenstein series 24 24 0

Trace form

\( 1392 q - 13 q^{2} - 531454 q^{3} + 1946157043 q^{4} - 288173102 q^{5} - 2418155530 q^{6} + 55218840866 q^{7} + 111518687680 q^{8} + 37461273447702 q^{9} + O(q^{10}) \) \( 1392 q - 13 q^{2} - 531454 q^{3} + 1946157043 q^{4} - 288173102 q^{5} - 2418155530 q^{6} + 55218840866 q^{7} + 111518687680 q^{8} + 37461273447702 q^{9} + 918803280808 q^{10} - 29212609707795 q^{11} - 339299845531339 q^{12} - 136259290951854 q^{13} - 2037452755030539 q^{14} - 1245192896814172 q^{15} + 31457322878578615 q^{16} + 2518058904994073 q^{17} - 2653510812682168 q^{18} + 51384186091294805 q^{19} + 69272013043707530 q^{20} - 8085415409820798 q^{21} + 360163015724130130 q^{22} - 77638006445811825 q^{23} - 454067315971449908 q^{24} + 6778873653905875644 q^{25} - 4556055981067121538 q^{26} + 5801015420315226167 q^{27} + 1222949528318209328 q^{28} - 5573387774038378884 q^{29} - 1908943711618433871 q^{30} + 22240457600728050691 q^{31} - 17293546002071984355 q^{32} + 11546953084647657026 q^{33} - 105910548394984482590 q^{34} + 154247743330832849040 q^{35} - 895754808599312649076 q^{36} + 401301442781946269935 q^{37} + 31900466416329032732 q^{38} + 213396002360190165145 q^{39} - 187831956889853046246 q^{40} + 568256831296107107574 q^{41} - 3210189761902459025102 q^{42} - 75996973992333217630 q^{43} + 1717201573274862466546 q^{44} - 2162939398983569048073 q^{45} + 5329546732755482202888 q^{46} + 2469521842809892214421 q^{47} + 3285672706165513480516 q^{48} + 820900208993390444058 q^{49} - 811432694043578129000 q^{50} - 6006409813143225983220 q^{51} - 21742610560356407493030 q^{52} - 4514769085932213529669 q^{53} - 8746803317568585445239 q^{54} - 51457853340903960364855 q^{55} - 72893340945423628038136 q^{56} + 19552316297874319918548 q^{57} + 37969469668690039337356 q^{58} - 77241069830277098700220 q^{59} + 121470710752948527056254 q^{60} - 240993208585340388402169 q^{61} + 386133947655389176216022 q^{62} - 316930774485513806693565 q^{63} - 1352914285717798536399412 q^{64} + 34204539769144536630398 q^{65} + 669981521458299183493332 q^{66} - 169704741068714994756869 q^{67} + 338897340291944529950477 q^{68} - 162097481170930241355482 q^{69} + 794636474080899560682670 q^{70} + 729669134348166720438883 q^{71} - 509688089147097288454360 q^{72} - 326518909815542571502473 q^{73} + 419904952183060837002754 q^{74} + 2532376073373684604692864 q^{75} + 976668649648356154993615 q^{76} + 663096292727170547861287 q^{77} - 4560096591846342266626032 q^{78} + 81513604898624061274175 q^{79} + 3335068343629988149115428 q^{80} + 7143988725021390242195728 q^{81} - 4905486373500988164554 q^{82} + 12459256241611815655790400 q^{83} - 16454781537898447524665276 q^{84} + 592239585092303368729798 q^{85} + 14207661934290291225126783 q^{86} + 5896620796266322557243088 q^{87} - 30748680631254059616355367 q^{88} - 13158777679326635788461470 q^{89} + 61101351319862600717576844 q^{90} - 6238991589320766337020988 q^{91} - 29092949910573662559673118 q^{92} - 52402554642167853027769280 q^{93} + 20134179318159580274523734 q^{94} + 49796831206322158602356435 q^{95} - 113650418426648785698213918 q^{96} - 79453968642084939842467360 q^{97} - 66180804945913382280924221 q^{98} + 40310339478549538434400208 q^{99} + O(q^{100}) \)

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

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