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Properties

Label 22.8
Level 22
Weight 8
Dimension 33
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 240
Trace bound 1

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(240\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(22))\).

Total New Old
Modular forms 115 33 82
Cusp forms 95 33 62
Eisenstein series 20 0 20

Trace form

\( 33 q + 16 q^{2} - 24 q^{3} - 128 q^{4} + 420 q^{5} - 1528 q^{6} - 62 q^{7} + 1024 q^{8} - 1654 q^{9} + O(q^{10}) \) \( 33 q + 16 q^{2} - 24 q^{3} - 128 q^{4} + 420 q^{5} - 1528 q^{6} - 62 q^{7} + 1024 q^{8} - 1654 q^{9} - 13360 q^{10} - 7682 q^{11} + 6784 q^{12} + 21166 q^{13} + 38736 q^{14} - 65650 q^{15} - 8192 q^{16} - 41572 q^{17} + 27752 q^{18} + 85115 q^{19} + 26880 q^{20} - 209604 q^{21} + 8736 q^{22} + 68636 q^{23} - 97792 q^{24} + 110450 q^{25} + 154432 q^{26} + 871185 q^{27} + 85632 q^{28} + 173200 q^{29} - 272400 q^{30} - 970594 q^{31} - 98304 q^{32} - 1654139 q^{33} - 49024 q^{34} + 646860 q^{35} + 440384 q^{36} + 772888 q^{37} + 1084400 q^{38} + 1903562 q^{39} - 281600 q^{40} - 2305184 q^{41} - 1304368 q^{42} - 4069054 q^{43} - 1247808 q^{44} + 756650 q^{45} + 1804832 q^{46} + 2547568 q^{47} - 98304 q^{48} + 6133654 q^{49} + 557520 q^{50} + 4135981 q^{51} - 1773056 q^{52} - 5599714 q^{53} - 7110720 q^{54} - 10430050 q^{55} + 1040384 q^{56} + 7045755 q^{57} + 666400 q^{58} + 6539165 q^{59} + 4711680 q^{60} + 17026786 q^{61} + 7271792 q^{62} - 6920264 q^{63} - 524288 q^{64} - 22046900 q^{65} - 6467168 q^{66} - 18094262 q^{67} - 2660608 q^{68} + 18627102 q^{69} + 16070080 q^{70} + 23209856 q^{71} - 1364992 q^{72} - 3518884 q^{73} - 3024704 q^{74} - 23153945 q^{75} + 722560 q^{76} - 24491212 q^{77} - 13123136 q^{78} - 14453270 q^{79} + 1761280 q^{80} + 34377303 q^{81} + 3761992 q^{82} - 4474939 q^{83} - 6388736 q^{84} - 7142610 q^{85} - 1219928 q^{86} + 26393380 q^{87} - 726016 q^{88} + 45386600 q^{89} + 8439120 q^{90} + 18955236 q^{91} + 6205824 q^{92} - 36100858 q^{93} + 12835936 q^{94} - 30295450 q^{95} + 786432 q^{96} - 42586727 q^{97} - 39014232 q^{98} - 22712954 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(22))\)

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
22.8.a \(\chi_{22}(1, \cdot)\) 22.8.a.a 1 1
22.8.a.b 1
22.8.a.c 1
22.8.a.d 2
22.8.c \(\chi_{22}(3, \cdot)\) 22.8.c.a 12 4
22.8.c.b 16

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(22)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)