Properties

Label 49.26
Level 49
Weight 26
Dimension 2327
Nonzero newspaces 4
Sturm bound 5096
Trace bound 1

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Defining parameters

Level: \( N \) = \( 49 = 7^{2} \)
Weight: \( k \) = \( 26 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(5096\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(49))\).

Total New Old
Modular forms 2480 2376 104
Cusp forms 2420 2327 93
Eisenstein series 60 49 11

Trace form

\( 2327 q - 63 q^{2} + 867063 q^{3} + 100665585 q^{4} + 458659101 q^{5} + 26130786615 q^{6} + 2296956466 q^{7} - 1154435188389 q^{8} + 5186894453106 q^{9} + O(q^{10}) \) \( 2327 q - 63 q^{2} + 867063 q^{3} + 100665585 q^{4} + 458659101 q^{5} + 26130786615 q^{6} + 2296956466 q^{7} - 1154435188389 q^{8} + 5186894453106 q^{9} + 17548837850895 q^{10} - 6723591411537 q^{11} - 161931179944233 q^{12} + 113600103900213 q^{13} - 842496158346318 q^{14} + 3801808272650337 q^{15} - 407479001014647 q^{16} - 5743634760288543 q^{17} - 15882234902094507 q^{18} - 31540333012763577 q^{19} - 37694195185305813 q^{20} + 6862021405218231 q^{21} + 439058069085657777 q^{22} - 274185413001831597 q^{23} - 559139099526643257 q^{24} + 990655637549604552 q^{25} - 6623334607163312157 q^{26} + 11933460223858362339 q^{27} - 9710795388567692762 q^{28} + 10688671488212400339 q^{29} - 11460625762115581089 q^{30} - 40356677859323442357 q^{31} - 25295232280084845843 q^{32} + 48338075414493082587 q^{33} - 141526637712112785969 q^{34} + 89611193295008985621 q^{35} - 876899094047735007609 q^{36} + 489982406709742940609 q^{37} + 151384900872909448347 q^{38} - 478761486328481409102 q^{39} + 581952020070540530283 q^{40} + 1052121229030116264831 q^{41} - 2788452540818290650171 q^{42} - 196499951535484073037 q^{43} + 1931797591177552371171 q^{44} - 3805347844645973867316 q^{45} + 2879279421507308102127 q^{46} - 1520842270022460014415 q^{47} - 75008839377603122982 q^{48} + 640137696807983632888 q^{49} + 8234475348271958254650 q^{50} + 8061402761912293273071 q^{51} - 23591589624173668832077 q^{52} - 3839138507104446037149 q^{53} - 1747977400782046151961 q^{54} + 40070227192492595773770 q^{55} - 13498411584616539650916 q^{56} - 105721313638755149253921 q^{57} + 39423780197665214394855 q^{58} + 97972709205406209495189 q^{59} - 81576374558968673177325 q^{60} - 117929250721114823283820 q^{61} + 427168422726922477032603 q^{62} - 217640937828695351362518 q^{63} - 1234056050463494468870313 q^{64} + 265811485495560054345351 q^{65} + 572054457981868663145919 q^{66} - 763616481301527892832073 q^{67} - 1270925714765129756036025 q^{68} + 2036728695554966775302475 q^{69} - 677431456343875567470927 q^{70} + 835810250430713430048945 q^{71} + 248353816245314784646509 q^{72} + 170571504624569628952233 q^{73} + 2432777321698685148469035 q^{74} + 371700471427321673363583 q^{75} - 2191008451433539239904185 q^{76} - 142300263924247213683297 q^{77} + 2174979152732520686251161 q^{78} + 10097128890153987690939 q^{79} - 16605899028276347876129700 q^{80} + 8934797164069568261309538 q^{81} - 3973514779485929741875560 q^{82} + 8972257018890270451648659 q^{83} - 19506139902876922492080618 q^{84} + 836845982388451886268297 q^{85} + 3140014726469711662744914 q^{86} - 6784012895448382799618229 q^{87} - 25311542751108220177575972 q^{88} - 7367519123414643494237883 q^{89} + 55956109447648994560278378 q^{90} + 4273500157687410924405593 q^{91} - 3472905148197274998174798 q^{92} - 46301613794987678505870705 q^{93} + 40412628865603758154198200 q^{94} + 73107406928081399748740427 q^{95} - 71964033723653804133363102 q^{96} - 36172402037557686303512088 q^{97} - 83068888119102085030597788 q^{98} + 72932144166120989176555344 q^{99} + O(q^{100}) \)

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(49))\)

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
49.26.a \(\chi_{49}(1, \cdot)\) 49.26.a.a 1 1
49.26.a.b 1
49.26.a.c 6
49.26.a.d 7
49.26.a.e 12
49.26.a.f 16
49.26.a.g 16
49.26.a.h 24
49.26.c \(\chi_{49}(18, \cdot)\) n/a 162 2
49.26.e \(\chi_{49}(8, \cdot)\) n/a 690 6
49.26.g \(\chi_{49}(2, \cdot)\) n/a 1392 12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(49)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)