Properties

Label 169.4
Level 169
Weight 4
Dimension 3405
Nonzero newspaces 8
Newform subspaces 43
Sturm bound 9464
Trace bound 1

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Defining parameters

Level: \( N \) = \( 169 = 13^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 43 \)
Sturm bound: \(9464\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(169))\).

Total New Old
Modular forms 3663 3610 53
Cusp forms 3435 3405 30
Eisenstein series 228 205 23

Trace form

\( 3405q - 66q^{2} - 66q^{3} - 66q^{4} - 66q^{5} - 66q^{6} + 6q^{7} + 78q^{8} - 66q^{9} + O(q^{10}) \) \( 3405q - 66q^{2} - 66q^{3} - 66q^{4} - 66q^{5} - 66q^{6} + 6q^{7} + 78q^{8} - 66q^{9} - 246q^{10} - 186q^{11} - 534q^{12} - 216q^{13} - 366q^{14} - 210q^{15} - 66q^{16} + 312q^{17} + 1590q^{18} + 822q^{19} + 966q^{20} - 66q^{21} - 846q^{22} - 522q^{23} - 2178q^{24} - 804q^{25} - 822q^{26} - 1782q^{27} + 42q^{28} + 792q^{29} + 1086q^{30} + 558q^{31} + 1242q^{32} + 1134q^{33} + 1326q^{34} - 66q^{35} + 246q^{36} - 432q^{37} - 2790q^{38} - 144q^{39} + 306q^{40} + 876q^{41} + 1194q^{42} + 774q^{43} - 534q^{44} - 636q^{45} - 1722q^{46} - 330q^{47} + 702q^{48} - 2010q^{49} + 126q^{50} + 714q^{51} + 258q^{52} - 2022q^{53} - 1518q^{54} - 2874q^{55} - 2070q^{56} - 2394q^{57} - 2118q^{58} - 1050q^{59} - 2382q^{60} + 2196q^{61} + 5166q^{62} + 6294q^{63} + 9306q^{64} + 3987q^{65} + 8154q^{66} + 1758q^{67} - 2718q^{68} - 4122q^{69} - 4038q^{70} - 3954q^{71} - 5958q^{72} - 4386q^{73} - 5214q^{74} - 1302q^{75} + 3606q^{76} - 822q^{77} - 3018q^{78} + 1794q^{79} - 6846q^{80} - 990q^{81} - 7182q^{82} - 6930q^{83} - 4614q^{84} - 2100q^{85} + 5538q^{86} + 7734q^{87} + 810q^{88} + 7374q^{89} + 13794q^{90} + 2652q^{91} + 9474q^{92} + 8310q^{93} + 3366q^{94} + 3846q^{95} - 3174q^{96} - 3690q^{97} + 5382q^{98} - 10458q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(169))\)

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
169.4.a \(\chi_{169}(1, \cdot)\) 169.4.a.a 1 1
169.4.a.b 1
169.4.a.c 1
169.4.a.d 1
169.4.a.e 1
169.4.a.f 2
169.4.a.g 2
169.4.a.h 2
169.4.a.i 2
169.4.a.j 2
169.4.a.k 9
169.4.a.l 9
169.4.b \(\chi_{169}(168, \cdot)\) 169.4.b.a 2 1
169.4.b.b 2
169.4.b.c 2
169.4.b.d 2
169.4.b.e 4
169.4.b.f 4
169.4.b.g 18
169.4.c \(\chi_{169}(22, \cdot)\) 169.4.c.a 2 2
169.4.c.b 2
169.4.c.c 2
169.4.c.d 2
169.4.c.e 2
169.4.c.f 4
169.4.c.g 4
169.4.c.h 4
169.4.c.i 4
169.4.c.j 4
169.4.c.k 18
169.4.c.l 18
169.4.e \(\chi_{169}(23, \cdot)\) 169.4.e.a 2 2
169.4.e.b 2
169.4.e.c 4
169.4.e.d 4
169.4.e.e 4
169.4.e.f 8
169.4.e.g 8
169.4.e.h 36
169.4.g \(\chi_{169}(14, \cdot)\) 169.4.g.a 540 12
169.4.h \(\chi_{169}(12, \cdot)\) 169.4.h.a 528 12
169.4.i \(\chi_{169}(3, \cdot)\) 169.4.i.a 1080 24
169.4.k \(\chi_{169}(4, \cdot)\) 169.4.k.a 1056 24

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(169))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(169)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)