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Properties

Label 184.6
Level 184
Weight 6
Dimension 2916
Nonzero newspaces 6
Sturm bound 12672
Trace bound 3

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Defining parameters

Level: \( N \) = \( 184 = 2^{3} \cdot 23 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(12672\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(184))\).

Total New Old
Modular forms 5412 3000 2412
Cusp forms 5148 2916 2232
Eisenstein series 264 84 180

Trace form

\( 2916 q - 18 q^{2} - 62 q^{3} - 62 q^{4} + 148 q^{5} + 210 q^{6} - 166 q^{7} + 474 q^{8} - 30 q^{9} + O(q^{10}) \) \( 2916 q - 18 q^{2} - 62 q^{3} - 62 q^{4} + 148 q^{5} + 210 q^{6} - 166 q^{7} + 474 q^{8} - 30 q^{9} - 1286 q^{10} - 270 q^{11} - 3174 q^{12} - 956 q^{13} + 4746 q^{14} + 3770 q^{15} + 6602 q^{16} + 1952 q^{17} - 9530 q^{18} - 6110 q^{19} - 9270 q^{20} + 960 q^{21} + 11250 q^{22} - 2542 q^{23} + 15540 q^{24} - 7858 q^{25} - 11238 q^{26} + 3418 q^{27} - 10326 q^{28} + 6564 q^{29} + 4234 q^{30} + 37290 q^{31} - 10838 q^{32} - 300 q^{33} + 9522 q^{34} - 19524 q^{35} + 20306 q^{36} + 51464 q^{37} - 31982 q^{38} - 27970 q^{39} - 32086 q^{40} + 27546 q^{41} + 52266 q^{42} - 41002 q^{43} + 58202 q^{44} - 110414 q^{45} - 29222 q^{46} - 11016 q^{47} - 71254 q^{48} - 7368 q^{49} + 94974 q^{50} + 118782 q^{51} + 73098 q^{52} + 48590 q^{53} - 46598 q^{54} + 286 q^{55} - 81558 q^{56} - 89624 q^{57} - 7590 q^{58} - 192284 q^{59} - 5206 q^{60} + 36964 q^{61} - 69014 q^{62} + 314394 q^{63} + 83818 q^{64} + 109740 q^{65} - 81124 q^{66} + 31042 q^{67} - 20710 q^{68} - 3680 q^{69} + 137812 q^{70} - 349478 q^{71} + 166522 q^{72} - 70224 q^{73} + 511508 q^{74} + 800964 q^{75} + 361200 q^{76} + 5952 q^{77} - 730114 q^{78} - 65364 q^{79} - 1512784 q^{80} - 935858 q^{81} - 1198898 q^{82} - 461516 q^{83} - 1283794 q^{84} - 220798 q^{85} + 382598 q^{86} + 238016 q^{87} + 1293434 q^{88} + 478586 q^{89} + 2988776 q^{90} + 1116036 q^{91} + 1670456 q^{92} + 229120 q^{93} + 1460588 q^{94} + 1593150 q^{95} + 1335212 q^{96} + 116490 q^{97} - 188514 q^{98} - 1050936 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(184))\)

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
184.6.a \(\chi_{184}(1, \cdot)\) 184.6.a.a 6 1
184.6.a.b 7
184.6.a.c 7
184.6.a.d 8
184.6.b \(\chi_{184}(93, \cdot)\) n/a 110 1
184.6.c \(\chi_{184}(183, \cdot)\) None 0 1
184.6.h \(\chi_{184}(91, \cdot)\) n/a 118 1
184.6.i \(\chi_{184}(9, \cdot)\) n/a 300 10
184.6.j \(\chi_{184}(11, \cdot)\) n/a 1180 10
184.6.o \(\chi_{184}(7, \cdot)\) None 0 10
184.6.p \(\chi_{184}(13, \cdot)\) n/a 1180 10

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(184))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(184)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 2}\)