Properties

Label 121.4
Level 121
Weight 4
Dimension 1715
Nonzero newspaces 4
Newform subspaces 20
Sturm bound 4840
Trace bound 1

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Defining parameters

Level: \( N \) = \( 121 = 11^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 20 \)
Sturm bound: \(4840\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(121))\).

Total New Old
Modular forms 1895 1856 39
Cusp forms 1735 1715 20
Eisenstein series 160 141 19

Trace form

\( 1715 q - 45 q^{2} - 45 q^{3} - 45 q^{4} - 45 q^{5} + 55 q^{6} - 25 q^{7} - 125 q^{8} - 205 q^{9} + O(q^{10}) \) \( 1715 q - 45 q^{2} - 45 q^{3} - 45 q^{4} - 45 q^{5} + 55 q^{6} - 25 q^{7} - 125 q^{8} - 205 q^{9} - 235 q^{10} - 100 q^{11} - 405 q^{12} - 85 q^{13} + 345 q^{14} + 575 q^{15} + 715 q^{16} + 255 q^{17} - 35 q^{18} - 495 q^{19} - 915 q^{20} - 875 q^{21} - 680 q^{22} + 115 q^{23} + 335 q^{24} + 75 q^{25} + 305 q^{26} + 165 q^{27} + 285 q^{28} + 55 q^{29} + 705 q^{30} + 735 q^{31} - 495 q^{32} + 155 q^{33} + 595 q^{34} - 185 q^{35} - 135 q^{36} - 325 q^{37} - 815 q^{38} - 1585 q^{39} - 135 q^{40} - 1065 q^{41} - 115 q^{42} + 1365 q^{43} + 1065 q^{44} - 1865 q^{45} - 1835 q^{46} - 1225 q^{47} - 2895 q^{48} - 2025 q^{49} - 225 q^{50} + 765 q^{51} + 2245 q^{52} + 3915 q^{53} + 6365 q^{54} + 1550 q^{55} + 2775 q^{56} + 2765 q^{57} - 2455 q^{58} - 2675 q^{59} - 3455 q^{60} - 685 q^{61} - 5235 q^{62} - 415 q^{63} - 1445 q^{64} - 1875 q^{65} - 1355 q^{66} - 1785 q^{67} - 2755 q^{68} - 1895 q^{69} - 335 q^{70} - 985 q^{71} - 405 q^{72} + 5055 q^{73} + 2885 q^{74} + 1305 q^{75} - 435 q^{76} + 2180 q^{77} + 3455 q^{78} + 1035 q^{79} + 6865 q^{80} + 2585 q^{81} + 5915 q^{82} - 1095 q^{83} + 1585 q^{84} - 5725 q^{85} - 1865 q^{86} - 7075 q^{87} - 4730 q^{88} - 3985 q^{89} + 245 q^{90} - 2885 q^{91} + 4925 q^{92} + 5375 q^{93} + 525 q^{94} - 3325 q^{95} - 655 q^{96} - 1755 q^{97} - 3795 q^{98} - 1670 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)

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
121.4.a \(\chi_{121}(1, \cdot)\) 121.4.a.a 1 1
121.4.a.b 2
121.4.a.c 2
121.4.a.d 2
121.4.a.e 2
121.4.a.f 4
121.4.a.g 4
121.4.a.h 6
121.4.c \(\chi_{121}(3, \cdot)\) 121.4.c.a 4 4
121.4.c.b 8
121.4.c.c 8
121.4.c.d 8
121.4.c.e 8
121.4.c.f 8
121.4.c.g 8
121.4.c.h 8
121.4.c.i 8
121.4.c.j 24
121.4.e \(\chi_{121}(12, \cdot)\) 121.4.e.a 320 10
121.4.g \(\chi_{121}(4, \cdot)\) 121.4.g.a 1280 40

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(121))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(121)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 1}\)