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Properties

Label 182.2
Level 182
Weight 2
Dimension 321
Nonzero newspaces 15
Newform subspaces 34
Sturm bound 4032
Trace bound 9

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Defining parameters

Level: \( N \) = \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 15 \)
Newform subspaces: \( 34 \)
Sturm bound: \(4032\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(182))\).

Total New Old
Modular forms 1152 321 831
Cusp forms 865 321 544
Eisenstein series 287 0 287

Trace form

\( 321 q + 3 q^{2} + 8 q^{3} - q^{4} + 6 q^{5} - 5 q^{7} - 3 q^{8} - 21 q^{9} + O(q^{10}) \) \( 321 q + 3 q^{2} + 8 q^{3} - q^{4} + 6 q^{5} - 5 q^{7} - 3 q^{8} - 21 q^{9} - 24 q^{10} - 12 q^{11} - 31 q^{13} - 9 q^{14} - 24 q^{15} - 9 q^{16} - 24 q^{17} - 15 q^{18} - 40 q^{19} - 20 q^{21} + 12 q^{22} + 11 q^{25} + 9 q^{26} - 40 q^{27} - 5 q^{28} - 36 q^{29} - 24 q^{30} - 40 q^{31} + 3 q^{32} - 72 q^{33} - 18 q^{34} - 66 q^{35} - 37 q^{36} - 28 q^{37} - 48 q^{38} - 60 q^{39} + 6 q^{40} - 72 q^{41} - 36 q^{42} - 60 q^{43} - 36 q^{44} - 72 q^{45} - 24 q^{46} - 24 q^{47} + 8 q^{48} - 33 q^{49} - 33 q^{50} - 48 q^{51} + 3 q^{52} - 30 q^{53} - 24 q^{54} - 48 q^{55} - 9 q^{56} - 40 q^{57} - 36 q^{58} - 24 q^{59} - 24 q^{60} - 32 q^{61} - 48 q^{62} - 113 q^{63} - 7 q^{64} - 96 q^{65} - 48 q^{66} - 76 q^{67} - 144 q^{69} - 30 q^{70} - 72 q^{71} - 33 q^{72} - 82 q^{73} + 36 q^{74} - 24 q^{75} + 56 q^{76} + 108 q^{77} + 84 q^{78} + 160 q^{79} + 207 q^{81} + 240 q^{82} + 120 q^{83} + 148 q^{84} + 294 q^{85} + 156 q^{86} + 288 q^{87} + 12 q^{88} + 198 q^{89} + 318 q^{90} + 253 q^{91} + 120 q^{92} + 200 q^{93} + 264 q^{94} + 264 q^{95} + 350 q^{97} + 99 q^{98} + 372 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(182))\)

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
182.2.a \(\chi_{182}(1, \cdot)\) 182.2.a.a 1 1
182.2.a.b 1
182.2.a.c 1
182.2.a.d 1
182.2.a.e 1
182.2.d \(\chi_{182}(155, \cdot)\) 182.2.d.a 2 1
182.2.d.b 6
182.2.e \(\chi_{182}(107, \cdot)\) 182.2.e.a 2 2
182.2.e.b 2
182.2.e.c 6
182.2.e.d 10
182.2.f \(\chi_{182}(53, \cdot)\) 182.2.f.a 2 2
182.2.f.b 6
182.2.f.c 8
182.2.g \(\chi_{182}(29, \cdot)\) 182.2.g.a 2 2
182.2.g.b 2
182.2.g.c 2
182.2.g.d 2
182.2.g.e 4
182.2.h \(\chi_{182}(9, \cdot)\) 182.2.h.a 2 2
182.2.h.b 2
182.2.h.c 6
182.2.h.d 10
182.2.i \(\chi_{182}(83, \cdot)\) 182.2.i.a 24 2
182.2.m \(\chi_{182}(43, \cdot)\) 182.2.m.a 4 2
182.2.m.b 12
182.2.n \(\chi_{182}(25, \cdot)\) 182.2.n.a 4 2
182.2.n.b 12
182.2.o \(\chi_{182}(23, \cdot)\) 182.2.o.a 20 2
182.2.v \(\chi_{182}(121, \cdot)\) 182.2.v.a 20 2
182.2.w \(\chi_{182}(19, \cdot)\) 182.2.w.a 40 4
182.2.ba \(\chi_{182}(41, \cdot)\) 182.2.ba.a 32 4
182.2.bb \(\chi_{182}(5, \cdot)\) 182.2.bb.a 32 4
182.2.bc \(\chi_{182}(45, \cdot)\) 182.2.bc.a 40 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(182))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(182)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)