↑

Properties

Label 184.4
Level 184
Weight 4
Dimension 1732
Nonzero newspaces 6
Newform subspaces 15
Sturm bound 8448
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 184 = 2^{3} \cdot 23 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 15 \)
Sturm bound: \(8448\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(184))\).

Total New Old
Modular forms 3300 1816 1484
Cusp forms 3036 1732 1304
Eisenstein series 264 84 180

Trace form

\( 1732 q - 18 q^{2} - 14 q^{3} + 2 q^{4} + 4 q^{5} - 78 q^{6} - 38 q^{7} - 102 q^{8} - 18 q^{9} + O(q^{10}) \) \( 1732 q - 18 q^{2} - 14 q^{3} + 2 q^{4} + 4 q^{5} - 78 q^{6} - 38 q^{7} - 102 q^{8} - 18 q^{9} + 90 q^{10} + 66 q^{11} + 90 q^{12} - 44 q^{13} - 54 q^{14} - 262 q^{15} - 54 q^{16} - 88 q^{17} - 26 q^{18} - 110 q^{19} - 246 q^{20} + 192 q^{21} + 146 q^{22} + 338 q^{23} + 180 q^{24} + 146 q^{25} - 582 q^{26} - 326 q^{27} - 214 q^{28} - 396 q^{29} + 202 q^{30} - 598 q^{31} + 682 q^{32} - 732 q^{33} - 78 q^{34} - 1356 q^{35} - 46 q^{36} - 864 q^{37} + 370 q^{38} + 1406 q^{39} - 470 q^{40} + 1182 q^{41} + 426 q^{42} + 1590 q^{43} - 358 q^{44} + 2926 q^{45} - 326 q^{46} - 552 q^{47} - 1366 q^{48} + 2784 q^{49} + 30 q^{50} + 1038 q^{51} + 1098 q^{52} + 242 q^{53} - 1478 q^{54} - 1506 q^{55} + 618 q^{56} - 4304 q^{57} + 1658 q^{58} - 1700 q^{59} + 1322 q^{60} - 1100 q^{61} + 874 q^{62} + 474 q^{63} - 1174 q^{64} - 2196 q^{65} + 908 q^{66} - 398 q^{67} - 358 q^{68} - 224 q^{69} - 940 q^{70} - 1190 q^{71} + 58 q^{72} + 824 q^{73} + 2132 q^{74} + 10956 q^{75} + 15584 q^{76} + 2112 q^{77} + 18878 q^{78} + 7436 q^{79} + 10784 q^{80} + 6106 q^{81} - 434 q^{82} - 1748 q^{83} - 11698 q^{84} - 3034 q^{85} - 8794 q^{86} - 15856 q^{87} - 14598 q^{88} - 8146 q^{89} - 37336 q^{90} - 13068 q^{91} - 19864 q^{92} - 1280 q^{93} - 15508 q^{94} - 8706 q^{95} - 28804 q^{96} - 7090 q^{97} - 9762 q^{98} - 7920 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(184))\)

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
184.4.a \(\chi_{184}(1, \cdot)\) 184.4.a.a 1 1
184.4.a.b 1
184.4.a.c 3
184.4.a.d 3
184.4.a.e 4
184.4.a.f 4
184.4.b \(\chi_{184}(93, \cdot)\) 184.4.b.a 30 1
184.4.b.b 36
184.4.c \(\chi_{184}(183, \cdot)\) None 0 1
184.4.h \(\chi_{184}(91, \cdot)\) 184.4.h.a 2 1
184.4.h.b 4
184.4.h.c 64
184.4.i \(\chi_{184}(9, \cdot)\) 184.4.i.a 90 10
184.4.i.b 90
184.4.j \(\chi_{184}(11, \cdot)\) 184.4.j.a 700 10
184.4.o \(\chi_{184}(7, \cdot)\) None 0 10
184.4.p \(\chi_{184}(13, \cdot)\) 184.4.p.a 700 10

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(184))\) into lower level spaces

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