Properties

Label 184.2
Level 184
Weight 2
Dimension 550
Nonzero newspaces 6
Newform subspaces 15
Sturm bound 4224
Trace bound 3

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Defining parameters

Level: \( N \) = \( 184 = 2^{3} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 15 \)
Sturm bound: \(4224\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(184))\).

Total New Old
Modular forms 1188 634 554
Cusp forms 925 550 375
Eisenstein series 263 84 179

Trace form

\( 550 q - 22 q^{2} - 22 q^{3} - 22 q^{4} - 22 q^{6} - 22 q^{7} - 22 q^{8} - 44 q^{9} + O(q^{10}) \) \( 550 q - 22 q^{2} - 22 q^{3} - 22 q^{4} - 22 q^{6} - 22 q^{7} - 22 q^{8} - 44 q^{9} - 22 q^{10} - 22 q^{11} - 22 q^{12} - 22 q^{14} - 22 q^{15} - 22 q^{16} - 44 q^{17} - 22 q^{18} - 22 q^{19} - 22 q^{20} - 22 q^{22} - 22 q^{23} - 44 q^{24} - 44 q^{25} - 22 q^{26} - 22 q^{27} - 22 q^{28} - 22 q^{30} - 22 q^{31} - 22 q^{32} - 44 q^{33} - 22 q^{34} - 44 q^{35} - 22 q^{36} - 44 q^{37} - 22 q^{38} - 66 q^{39} - 22 q^{40} - 66 q^{41} - 22 q^{42} - 66 q^{43} - 22 q^{44} - 66 q^{45} - 22 q^{46} - 88 q^{47} - 22 q^{48} - 110 q^{49} - 22 q^{50} - 66 q^{51} - 22 q^{52} - 22 q^{53} - 22 q^{54} - 66 q^{55} - 22 q^{56} - 88 q^{57} - 22 q^{58} - 44 q^{59} - 22 q^{60} - 22 q^{62} - 22 q^{63} - 22 q^{64} - 44 q^{65} + 44 q^{66} - 22 q^{67} - 22 q^{68} - 44 q^{70} - 22 q^{71} - 22 q^{72} - 44 q^{73} + 44 q^{75} + 88 q^{76} + 198 q^{78} + 44 q^{79} + 176 q^{80} + 88 q^{81} + 110 q^{82} + 44 q^{83} + 286 q^{84} + 66 q^{85} + 198 q^{86} + 176 q^{87} + 154 q^{88} + 22 q^{89} + 396 q^{90} + 132 q^{91} + 176 q^{92} + 176 q^{94} + 110 q^{95} + 396 q^{96} + 22 q^{97} + 154 q^{98} + 176 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)

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
184.2.a \(\chi_{184}(1, \cdot)\) 184.2.a.a 1 1
184.2.a.b 1
184.2.a.c 1
184.2.a.d 1
184.2.a.e 2
184.2.b \(\chi_{184}(93, \cdot)\) 184.2.b.a 2 1
184.2.b.b 8
184.2.b.c 12
184.2.c \(\chi_{184}(183, \cdot)\) None 0 1
184.2.h \(\chi_{184}(91, \cdot)\) 184.2.h.a 4 1
184.2.h.b 6
184.2.h.c 12
184.2.i \(\chi_{184}(9, \cdot)\) 184.2.i.a 30 10
184.2.i.b 30
184.2.j \(\chi_{184}(11, \cdot)\) 184.2.j.a 220 10
184.2.o \(\chi_{184}(7, \cdot)\) None 0 10
184.2.p \(\chi_{184}(13, \cdot)\) 184.2.p.a 220 10

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(184))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(184)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 1}\)