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Properties

Label 182.4
Level 182
Weight 4
Dimension 954
Nonzero newspaces 15
Newform subspaces 36
Sturm bound 8064
Trace bound 7

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Defining parameters

Level: \( N \) = \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 15 \)
Newform subspaces: \( 36 \)
Sturm bound: \(8064\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(182))\).

Total New Old
Modular forms 3168 954 2214
Cusp forms 2880 954 1926
Eisenstein series 288 0 288

Trace form

\( 954 q - 24 q^{3} + 48 q^{5} + 72 q^{6} + 24 q^{7} - 48 q^{8} - 84 q^{9} + O(q^{10}) \) \( 954 q - 24 q^{3} + 48 q^{5} + 72 q^{6} + 24 q^{7} - 48 q^{8} - 84 q^{9} + 108 q^{10} + 156 q^{11} + 510 q^{13} - 144 q^{14} + 312 q^{15} - 174 q^{17} - 204 q^{18} - 1248 q^{19} - 24 q^{20} + 24 q^{21} + 432 q^{22} + 1044 q^{23} + 96 q^{24} + 330 q^{25} - 348 q^{26} + 504 q^{27} - 528 q^{28} - 3258 q^{29} - 1968 q^{30} - 1548 q^{31} + 228 q^{33} + 1680 q^{34} + 1620 q^{35} + 1872 q^{36} + 1290 q^{37} + 2520 q^{38} + 3060 q^{39} - 288 q^{40} + 4302 q^{41} + 288 q^{42} + 1368 q^{43} + 48 q^{44} - 54 q^{45} - 528 q^{46} - 1668 q^{47} + 192 q^{48} - 1656 q^{49} - 5436 q^{50} - 11148 q^{51} - 2016 q^{52} - 4692 q^{53} - 3024 q^{54} - 2664 q^{55} - 192 q^{56} + 504 q^{57} + 2196 q^{58} + 2856 q^{59} + 3120 q^{60} - 354 q^{61} + 3936 q^{62} + 816 q^{63} - 384 q^{64} + 1686 q^{65} + 6720 q^{66} + 6588 q^{67} + 1512 q^{68} + 10416 q^{69} + 2736 q^{70} + 6000 q^{71} + 1728 q^{72} + 9540 q^{73} + 4308 q^{74} + 19332 q^{75} + 3120 q^{76} + 12492 q^{77} - 3312 q^{78} + 2556 q^{79} - 288 q^{80} - 3912 q^{81} - 2940 q^{82} + 756 q^{83} - 4896 q^{84} - 17178 q^{85} - 8400 q^{86} - 28320 q^{87} - 2688 q^{88} - 28044 q^{89} - 26376 q^{90} - 26826 q^{91} - 7584 q^{92} - 30132 q^{93} - 17088 q^{94} - 20316 q^{95} + 384 q^{96} - 12360 q^{97} - 4224 q^{98} - 11400 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(182))\)

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
182.4.a \(\chi_{182}(1, \cdot)\) 182.4.a.a 1 1
182.4.a.b 1
182.4.a.c 1
182.4.a.d 1
182.4.a.e 2
182.4.a.f 2
182.4.a.g 2
182.4.a.h 2
182.4.a.i 3
182.4.a.j 3
182.4.d \(\chi_{182}(155, \cdot)\) 182.4.d.a 2 1
182.4.d.b 6
182.4.d.c 12
182.4.e \(\chi_{182}(107, \cdot)\) 182.4.e.a 28 2
182.4.e.b 28
182.4.f \(\chi_{182}(53, \cdot)\) 182.4.f.a 2 2
182.4.f.b 6
182.4.f.c 10
182.4.f.d 14
182.4.f.e 16
182.4.g \(\chi_{182}(29, \cdot)\) 182.4.g.a 8 2
182.4.g.b 10
182.4.g.c 12
182.4.g.d 14
182.4.h \(\chi_{182}(9, \cdot)\) 182.4.h.a 28 2
182.4.h.b 28
182.4.i \(\chi_{182}(83, \cdot)\) 182.4.i.a 56 2
182.4.m \(\chi_{182}(43, \cdot)\) 182.4.m.a 16 2
182.4.m.b 24
182.4.n \(\chi_{182}(25, \cdot)\) 182.4.n.a 56 2
182.4.o \(\chi_{182}(23, \cdot)\) 182.4.o.a 56 2
182.4.v \(\chi_{182}(121, \cdot)\) 182.4.v.a 56 2
182.4.w \(\chi_{182}(19, \cdot)\) 182.4.w.a 112 4
182.4.ba \(\chi_{182}(41, \cdot)\) 182.4.ba.a 112 4
182.4.bb \(\chi_{182}(5, \cdot)\) 182.4.bb.a 112 4
182.4.bc \(\chi_{182}(45, \cdot)\) 182.4.bc.a 112 4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(182))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(182)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)