Properties

Label 261.12
Level 261
Weight 12
Dimension 21771
Nonzero newspaces 12
Sturm bound 60480
Trace bound 2

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Defining parameters

Level: \( N \) = \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(60480\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(261))\).

Total New Old
Modular forms 27944 22013 5931
Cusp forms 27496 21771 5725
Eisenstein series 448 242 206

Trace form

\( 21771 q + 132 q^{2} - 32 q^{3} + 11376 q^{4} + 13338 q^{5} - 41222 q^{6} - 160458 q^{7} + 537282 q^{8} - 271064 q^{9} + O(q^{10}) \) \( 21771 q + 132 q^{2} - 32 q^{3} + 11376 q^{4} + 13338 q^{5} - 41222 q^{6} - 160458 q^{7} + 537282 q^{8} - 271064 q^{9} - 1196670 q^{10} + 2570406 q^{11} - 2055776 q^{12} - 3987006 q^{13} + 4276278 q^{14} + 12717160 q^{15} + 24804024 q^{16} - 63174786 q^{17} - 17365808 q^{18} + 44847858 q^{19} + 149870190 q^{20} - 110024468 q^{21} - 5132408 q^{22} + 308929256 q^{23} + 422200654 q^{24} - 409249886 q^{25} - 1056247282 q^{26} + 167398648 q^{27} + 1151563644 q^{28} + 465098404 q^{29} + 47165072 q^{30} - 1270356182 q^{31} - 1942548616 q^{32} - 62676740 q^{33} + 3226127948 q^{34} + 1910595994 q^{35} + 39969250 q^{36} - 2051078824 q^{37} - 6642654512 q^{38} + 3998129896 q^{39} + 6826407462 q^{40} + 1750161690 q^{41} - 8343937820 q^{42} - 2174948682 q^{43} - 6283670740 q^{44} - 3498698396 q^{45} - 23104369664 q^{46} - 3313026134 q^{47} + 18670472194 q^{48} + 25018234694 q^{49} + 40732134758 q^{50} - 3473554160 q^{51} - 49720691486 q^{52} - 52748098215 q^{53} - 36255715562 q^{54} + 3666088978 q^{55} + 84008956424 q^{56} + 15710848336 q^{57} + 100668882138 q^{58} + 46452442960 q^{59} + 20566712176 q^{60} - 60266964886 q^{61} - 274241028952 q^{62} - 103130413832 q^{63} + 44981648736 q^{64} + 135043715841 q^{65} + 186403656436 q^{66} + 99635347310 q^{67} + 166051838174 q^{68} - 13814585156 q^{69} - 497283118910 q^{70} - 712415761880 q^{71} - 140603386766 q^{72} + 408160571465 q^{73} + 595076207420 q^{74} + 315975390780 q^{75} - 763584642852 q^{76} - 495752324352 q^{77} - 621319137636 q^{78} - 38552858838 q^{79} + 833632651542 q^{80} + 367587749496 q^{81} + 506452402422 q^{82} + 321956386950 q^{83} + 915113200468 q^{84} - 448563010542 q^{85} - 1695695540226 q^{86} - 680393385852 q^{87} - 1261863542634 q^{88} - 834877728948 q^{89} - 67796267344 q^{90} + 1158063292926 q^{91} + 4268248168338 q^{92} + 1636459015196 q^{93} + 680698653030 q^{94} - 422579890170 q^{95} - 3671621625192 q^{96} - 662518692029 q^{97} - 4723733701508 q^{98} - 1282865708052 q^{99} + O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(261))\)

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
261.12.a \(\chi_{261}(1, \cdot)\) 261.12.a.a 11 1
261.12.a.b 11
261.12.a.c 12
261.12.a.d 14
261.12.a.e 14
261.12.a.f 15
261.12.a.g 26
261.12.a.h 26
261.12.c \(\chi_{261}(28, \cdot)\) n/a 136 1
261.12.e \(\chi_{261}(88, \cdot)\) n/a 616 2
261.12.g \(\chi_{261}(17, \cdot)\) n/a 220 2
261.12.i \(\chi_{261}(115, \cdot)\) n/a 656 2
261.12.k \(\chi_{261}(82, \cdot)\) n/a 822 6
261.12.l \(\chi_{261}(41, \cdot)\) n/a 1312 4
261.12.o \(\chi_{261}(64, \cdot)\) n/a 816 6
261.12.q \(\chi_{261}(7, \cdot)\) n/a 3936 12
261.12.r \(\chi_{261}(8, \cdot)\) n/a 1320 12
261.12.u \(\chi_{261}(4, \cdot)\) n/a 3936 12
261.12.x \(\chi_{261}(2, \cdot)\) n/a 7872 24

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

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(261))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(261)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)