Properties

Label 4.21
Level 4
Weight 21
Dimension 9
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 21
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 21 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(21\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(\Gamma_1(4))\).

Total New Old
Modular forms 11 11 0
Cusp forms 9 9 0
Eisenstein series 2 2 0

Trace form

\( 9 q - 628 q^{2} - 267504 q^{4} - 738494 q^{5} + 99460608 q^{6} + 1103532992 q^{8} - 6924577767 q^{9} + O(q^{10}) \) \( 9 q - 628 q^{2} - 267504 q^{4} - 738494 q^{5} + 99460608 q^{6} + 1103532992 q^{8} - 6924577767 q^{9} + 1611884376 q^{10} - 41779799040 q^{12} + 147660923874 q^{13} - 200556776448 q^{14} + 70138216704 q^{16} - 1684556709806 q^{17} + 1635822350412 q^{18} + 241483768096 q^{20} + 33281721747456 q^{21} - 31324969489920 q^{22} - 47563142934528 q^{24} - 567413012949 q^{25} - 63229698776360 q^{26} + 385881741772800 q^{28} + 303916348382242 q^{29} - 1063857826698240 q^{30} + 454535173225472 q^{32} + 1131041167426560 q^{33} - 4199565255965160 q^{34} + 16320708718416912 q^{36} - 7415248775263806 q^{37} - 19214136907706880 q^{38} + 42169382228654976 q^{40} - 5755597456531022 q^{41} - 92697489416232960 q^{42} + 157933848933319680 q^{44} + 22280783580364386 q^{45} - 271527229329687552 q^{46} + 485296685862666240 q^{48} - 37006326729654807 q^{49} - 623084159258016924 q^{50} + 813052968459434784 q^{52} + 132739492344115714 q^{53} - 1607547577815069696 q^{54} + 1749313578676543488 q^{56} + 440441203792112640 q^{57} - 1972695284657517096 q^{58} + 2279505537583872000 q^{60} - 1172450092804974942 q^{61} - 1243411198213386240 q^{62} + 1333510659266973696 q^{64} - 828610552028041948 q^{65} - 21993146403409920 q^{66} - 1641594099654542816 q^{68} + 3450619355851659264 q^{69} + 8506721176491632640 q^{70} - 19477455141526114368 q^{72} - 4955973119248806606 q^{73} + 23508341140743382360 q^{74} - 26576303558589158400 q^{76} - 5280312525070141440 q^{77} + 39300720744848010240 q^{78} - 53478714049403538944 q^{80} + 27869130702616624425 q^{81} + 59306974273770046104 q^{82} - 85636060864270565376 q^{84} + 5624508021574984452 q^{85} + 60721004056878217728 q^{86} - 36088003765030440960 q^{88} - 30717207683107545998 q^{89} + 14470051757664399576 q^{90} + 64932970344704317440 q^{92} - 53255995615294218240 q^{93} - 49076400009934399488 q^{94} + 148896006651003076608 q^{96} + 21227709255069480594 q^{97} - 274458557005261496308 q^{98} + O(q^{100}) \)

Decomposition of \(S_{21}^{\mathrm{new}}(\Gamma_1(4))\)

We only show spaces with odd 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
4.21.b \(\chi_{4}(3, \cdot)\) 4.21.b.a 1 1
4.21.b.b 8