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

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

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 the 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

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