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Properties

Label 169.10
Level 169
Weight 10
Dimension 10419
Nonzero newspaces 8
Sturm bound 23660
Trace bound 1

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Defining parameters

Level: \( N \) = \( 169 = 13^{2} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(23660\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(169))\).

Total New Old
Modular forms 10761 10624 137
Cusp forms 10533 10419 114
Eisenstein series 228 205 23

Trace form

\( 10419 q - 66 q^{2} - 66 q^{3} - 66 q^{4} - 66 q^{5} - 66 q^{6} + 4038 q^{7} + 73662 q^{8} - 66 q^{9} + O(q^{10}) \) \( 10419 q - 66 q^{2} - 66 q^{3} - 66 q^{4} - 66 q^{5} - 66 q^{6} + 4038 q^{7} + 73662 q^{8} - 66 q^{9} - 306786 q^{10} + 36774 q^{11} + 829386 q^{12} + 108360 q^{13} - 727806 q^{14} - 1193682 q^{15} - 66 q^{16} + 2815332 q^{17} - 1992198 q^{18} + 1891830 q^{19} - 95058 q^{20} - 2184066 q^{21} - 14502606 q^{22} - 2158314 q^{23} + 19398942 q^{24} + 11718696 q^{25} + 8735178 q^{26} - 6678774 q^{27} - 28478646 q^{28} - 48742500 q^{29} - 11197218 q^{30} + 43257486 q^{31} + 104870010 q^{32} + 34107534 q^{33} - 76366962 q^{34} - 125492706 q^{35} - 69537066 q^{36} + 107018004 q^{37} + 150129738 q^{38} + 80178864 q^{39} - 213193422 q^{40} - 113494152 q^{41} + 29052762 q^{42} + 160350054 q^{43} - 113669622 q^{44} - 146879016 q^{45} - 340457754 q^{46} + 12327606 q^{47} + 113874462 q^{48} + 69698166 q^{49} + 257217330 q^{50} + 143171274 q^{51} + 288763590 q^{52} + 228379434 q^{53} + 492983490 q^{54} - 327790074 q^{55} - 822907062 q^{56} - 1131415242 q^{57} - 1075604034 q^{58} - 308757690 q^{59} + 121664658 q^{60} + 1564547880 q^{61} + 2017677342 q^{62} - 201404202 q^{63} - 1101924774 q^{64} - 106769511 q^{65} + 2710233306 q^{66} + 2485367838 q^{67} + 672525450 q^{68} - 2199370122 q^{69} - 4608699990 q^{70} - 3093851250 q^{71} - 5102810694 q^{72} - 259608162 q^{73} + 1009589814 q^{74} + 2605971210 q^{75} + 4482522966 q^{76} + 4653806154 q^{77} + 3971344830 q^{78} + 1667535810 q^{79} - 6110622 q^{80} - 1428453054 q^{81} - 5229320154 q^{82} - 7686015858 q^{83} - 13626100902 q^{84} - 2534884032 q^{85} - 5986033374 q^{86} - 5033253642 q^{87} + 10703372970 q^{88} + 10695147534 q^{89} + 32397195858 q^{90} + 6798799020 q^{91} + 5434586946 q^{92} - 4784070234 q^{93} - 17332218762 q^{94} - 15243614778 q^{95} - 20018064966 q^{96} - 9419334330 q^{97} - 17393800026 q^{98} - 14821060410 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(169))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
169.10.a \(\chi_{169}(1, \cdot)\) 169.10.a.a 4 1
169.10.a.b 5
169.10.a.c 9
169.10.a.d 9
169.10.a.e 10
169.10.a.f 20
169.10.a.g 27
169.10.a.h 27
169.10.b \(\chi_{169}(168, \cdot)\) n/a 110 1
169.10.c \(\chi_{169}(22, \cdot)\) n/a 222 2
169.10.e \(\chi_{169}(23, \cdot)\) n/a 220 2
169.10.g \(\chi_{169}(14, \cdot)\) n/a 1620 12
169.10.h \(\chi_{169}(12, \cdot)\) n/a 1632 12
169.10.i \(\chi_{169}(3, \cdot)\) n/a 3240 24
169.10.k \(\chi_{169}(4, \cdot)\) n/a 3264 24

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(169))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(169)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 1}\)