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Properties

Label 13.12
Level 13
Weight 12
Dimension 69
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 168
Trace bound 1

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Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(168\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(13))\).

Total New Old
Modular forms 83 79 4
Cusp forms 71 69 2
Eisenstein series 12 10 2

Trace form

\( 69 q + 42 q^{2} - 510 q^{3} + 2938 q^{4} - 9666 q^{5} + 12090 q^{6} + 85096 q^{7} - 463878 q^{8} + 699672 q^{9} + O(q^{10}) \) \( 69 q + 42 q^{2} - 510 q^{3} + 2938 q^{4} - 9666 q^{5} + 12090 q^{6} + 85096 q^{7} - 463878 q^{8} + 699672 q^{9} - 1225926 q^{10} - 1160844 q^{11} + 5718516 q^{12} + 759616 q^{13} - 7409676 q^{14} - 5708994 q^{15} + 18997242 q^{16} + 13026063 q^{17} - 52966356 q^{18} - 63240242 q^{19} + 163762818 q^{20} - 1516404 q^{21} - 122035440 q^{22} - 90525714 q^{23} + 123197514 q^{24} + 197482813 q^{25} + 154830312 q^{26} - 132811104 q^{27} - 376184396 q^{28} - 474182019 q^{29} - 91481622 q^{30} + 702841408 q^{31} + 2437372284 q^{32} - 842130588 q^{33} - 2863583310 q^{34} - 1289507736 q^{35} + 1550423070 q^{36} - 261405821 q^{37} + 3364214196 q^{38} + 1396334706 q^{39} + 1137706332 q^{40} - 6605728833 q^{41} - 8546677188 q^{42} + 2680192908 q^{43} + 11175408420 q^{44} + 10902828609 q^{45} - 1311327354 q^{46} - 11213517984 q^{47} - 21019778742 q^{48} - 2237432942 q^{49} + 6304675248 q^{50} + 40031074908 q^{51} + 5601090300 q^{52} - 3631338504 q^{53} - 27965451384 q^{54} - 22829653272 q^{55} + 241340868 q^{56} - 260417628 q^{57} + 19479355242 q^{58} + 17900568672 q^{59} - 3286788768 q^{60} - 8951775817 q^{61} - 6180153126 q^{62} + 18858831768 q^{63} - 27845443220 q^{64} - 10339447365 q^{65} + 59370877896 q^{66} + 3917432458 q^{67} + 53885691204 q^{68} - 29885808432 q^{69} - 40146390540 q^{70} - 79874642994 q^{71} - 38954689140 q^{72} - 84166154582 q^{73} + 49164417198 q^{74} + 114013992792 q^{75} + 2663195662 q^{76} + 7244146008 q^{77} + 94143495732 q^{78} - 2236730344 q^{79} + 211371935064 q^{80} + 19178111292 q^{81} - 248187559242 q^{82} - 182906835876 q^{83} - 389541827220 q^{84} - 169103748729 q^{85} + 510254742408 q^{86} + 298302599250 q^{87} + 252113964324 q^{88} - 60177797802 q^{89} - 221083143216 q^{90} + 60190808704 q^{91} - 123197528268 q^{92} + 457523586552 q^{93} + 437233299294 q^{94} + 131470123998 q^{95} - 1393584363540 q^{96} - 733535874602 q^{97} - 81574359114 q^{98} - 191664641100 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(13))\)

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
13.12.a \(\chi_{13}(1, \cdot)\) 13.12.a.a 5 1
13.12.a.b 6
13.12.b \(\chi_{13}(12, \cdot)\) 13.12.b.a 12 1
13.12.c \(\chi_{13}(3, \cdot)\) 13.12.c.a 24 2
13.12.e \(\chi_{13}(4, \cdot)\) 13.12.e.a 22 2

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(13))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(13)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)