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Properties

Label 92.6
Level 92
Weight 6
Dimension 746
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 3168
Trace bound 1

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Defining parameters

Level: \( N \) = \( 92 = 2^{2} \cdot 23 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(3168\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(92))\).

Total New Old
Modular forms 1375 790 585
Cusp forms 1265 746 519
Eisenstein series 110 44 66

Trace form

\( 746 q - 11 q^{2} + 24 q^{3} - 11 q^{4} - 130 q^{5} - 11 q^{6} + 176 q^{7} - 11 q^{8} + 176 q^{9} + O(q^{10}) \) \( 746 q - 11 q^{2} + 24 q^{3} - 11 q^{4} - 130 q^{5} - 11 q^{6} + 176 q^{7} - 11 q^{8} + 176 q^{9} - 11 q^{10} - 1080 q^{11} - 11 q^{12} + 814 q^{13} - 11 q^{14} - 3335 q^{15} - 11 q^{16} + 2761 q^{17} - 11 q^{18} - 891 q^{19} - 11 q^{20} - 14641 q^{21} - 6038 q^{23} - 22 q^{24} - 286 q^{25} - 11 q^{26} + 13935 q^{27} - 11 q^{28} + 12397 q^{29} - 11 q^{30} - 8391 q^{31} - 11 q^{32} - 28323 q^{33} + 75999 q^{34} + 25454 q^{35} - 49016 q^{36} - 71542 q^{37} - 95766 q^{38} - 71412 q^{39} - 68211 q^{40} - 35156 q^{41} + 78199 q^{42} + 83556 q^{43} + 138974 q^{44} + 144342 q^{45} + 174141 q^{46} + 75676 q^{47} + 95821 q^{48} + 38234 q^{49} - 48136 q^{50} - 56628 q^{51} - 279301 q^{52} - 110972 q^{53} - 320771 q^{54} - 292642 q^{55} - 140316 q^{56} + 84359 q^{57} + 138534 q^{58} + 362826 q^{59} + 301939 q^{60} + 194634 q^{61} - 11 q^{62} - 10219 q^{63} - 11 q^{64} - 151305 q^{65} - 2684 q^{66} - 137982 q^{67} - 299795 q^{69} - 22 q^{70} - 82531 q^{71} + 2662 q^{72} - 145684 q^{73} - 273240 q^{74} + 524249 q^{75} - 280566 q^{76} + 355245 q^{77} + 539099 q^{78} + 339482 q^{79} + 791890 q^{80} - 709608 q^{81} + 438295 q^{82} - 293491 q^{83} + 445203 q^{84} - 540782 q^{85} - 172821 q^{86} + 226578 q^{87} - 479523 q^{88} + 393824 q^{89} - 1636338 q^{90} + 290796 q^{91} - 810722 q^{92} + 2095036 q^{93} - 631180 q^{94} - 283635 q^{95} - 551980 q^{96} - 31535 q^{97} + 211277 q^{98} + 121539 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(92))\)

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
92.6.a \(\chi_{92}(1, \cdot)\) 92.6.a.a 4 1
92.6.a.b 4
92.6.b \(\chi_{92}(91, \cdot)\) 92.6.b.a 6 1
92.6.b.b 52
92.6.e \(\chi_{92}(9, \cdot)\) 92.6.e.a 100 10
92.6.h \(\chi_{92}(7, \cdot)\) 92.6.h.a 580 10

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(92))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(92)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)