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Properties

Label 121.12
Level 121
Weight 12
Dimension 6476
Nonzero newspaces 4
Sturm bound 14520
Trace bound 1

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Defining parameters

Level: \( N \) = \( 121 = 11^{2} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(14520\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(121))\).

Total New Old
Modular forms 6735 6617 118
Cusp forms 6575 6476 99
Eisenstein series 160 141 19

Trace form

\( 6476 q - 69 q^{2} + 207 q^{3} - 1517 q^{4} + 4785 q^{5} + 56947 q^{6} - 208619 q^{7} + 555475 q^{8} + 207092 q^{9} + O(q^{10}) \) \( 6476 q - 69 q^{2} + 207 q^{3} - 1517 q^{4} + 4785 q^{5} + 56947 q^{6} - 208619 q^{7} + 555475 q^{8} + 207092 q^{9} - 2115955 q^{10} + 76295 q^{11} + 9991851 q^{12} - 607913 q^{13} - 23545599 q^{14} + 21308435 q^{15} + 10268731 q^{16} - 35678649 q^{17} + 38784457 q^{18} + 73849805 q^{19} - 60538275 q^{20} - 167583563 q^{21} - 59973560 q^{22} - 18438143 q^{23} + 697085135 q^{24} + 224182750 q^{25} - 1003020223 q^{26} - 894462945 q^{27} + 618695853 q^{28} + 1367207935 q^{29} + 1263559065 q^{30} - 1612644053 q^{31} - 1057420719 q^{32} - 1257412870 q^{33} + 3507245331 q^{34} + 3373616245 q^{35} - 1137832719 q^{36} - 2714882779 q^{37} - 3930853895 q^{38} + 3576007529 q^{39} + 4387437465 q^{40} + 4604244627 q^{41} - 7728783163 q^{42} - 5347880543 q^{43} - 4640260275 q^{44} + 5450295445 q^{45} + 2879742117 q^{46} + 4812581081 q^{47} + 13716662577 q^{48} + 5005796638 q^{49} - 6825256425 q^{50} - 10115184003 q^{51} - 45099991419 q^{52} + 9597090507 q^{53} + 74983534205 q^{54} + 6453086650 q^{55} - 77416106985 q^{56} - 81601387675 q^{57} + 55131812905 q^{58} + 30657987475 q^{59} + 127051596625 q^{60} + 26664451607 q^{61} - 599571723 q^{62} - 47026661863 q^{63} - 78029225397 q^{64} - 58157081115 q^{65} - 61725886235 q^{66} - 19387306239 q^{67} - 415874467 q^{68} + 41975390659 q^{69} + 282265464545 q^{70} + 142969395287 q^{71} + 46404962235 q^{72} + 58936322347 q^{73} - 206833686859 q^{74} - 198222460995 q^{75} - 445706162435 q^{76} - 62897946835 q^{77} - 36792651841 q^{78} + 94252986525 q^{79} + 494562974545 q^{80} + 193734918926 q^{81} + 33725875287 q^{82} + 648547643577 q^{83} + 518328331921 q^{84} - 174617796795 q^{85} - 696239504093 q^{86} - 1055585750815 q^{87} - 707408580450 q^{88} - 300375049165 q^{89} + 1114769967005 q^{90} + 810889302257 q^{91} + 759715604381 q^{92} + 998862474719 q^{93} + 1429492835261 q^{94} + 760000411025 q^{95} - 808698586063 q^{96} - 1498798684059 q^{97} - 3118486928727 q^{98} - 1208168903390 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(121))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
121.12.a \(\chi_{121}(1, \cdot)\) 121.12.a.a 1 1
121.12.a.b 1
121.12.a.c 3
121.12.a.d 5
121.12.a.e 8
121.12.a.f 9
121.12.a.g 9
121.12.a.h 20
121.12.a.i 20
121.12.a.j 20
121.12.c \(\chi_{121}(3, \cdot)\) n/a 380 4
121.12.e \(\chi_{121}(12, \cdot)\) n/a 1200 10
121.12.g \(\chi_{121}(4, \cdot)\) n/a 4800 40

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

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(121))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(121)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)