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Properties

Label 261.6
Level 261
Weight 6
Dimension 9831
Nonzero newspaces 12
Sturm bound 30240
Trace bound 2

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Defining parameters

Level: \( N \) = \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(30240\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(261))\).

Total New Old
Modular forms 12824 10073 2751
Cusp forms 12376 9831 2545
Eisenstein series 448 242 206

Trace form

\( 9831 q - 60 q^{2} - 32 q^{3} + 48 q^{4} - 186 q^{5} - 398 q^{6} - 18 q^{7} + 1794 q^{8} + 772 q^{9} + O(q^{10}) \) \( 9831 q - 60 q^{2} - 32 q^{3} + 48 q^{4} - 186 q^{5} - 398 q^{6} - 18 q^{7} + 1794 q^{8} + 772 q^{9} - 174 q^{10} - 2058 q^{11} - 5504 q^{12} - 954 q^{13} - 2346 q^{14} + 4048 q^{15} + 2808 q^{16} + 10434 q^{17} + 16144 q^{18} - 918 q^{19} - 27138 q^{20} - 17396 q^{21} + 7856 q^{22} - 11416 q^{23} - 1154 q^{24} + 8576 q^{25} + 28778 q^{26} + 20248 q^{27} - 40516 q^{28} - 28562 q^{29} - 44320 q^{30} - 16846 q^{31} - 232 q^{32} + 17584 q^{33} + 32992 q^{34} + 74458 q^{35} + 29122 q^{36} + 49900 q^{37} + 27688 q^{38} - 16496 q^{39} - 90762 q^{40} - 16278 q^{41} - 20252 q^{42} - 7146 q^{43} - 218260 q^{44} - 86132 q^{45} - 106256 q^{46} + 15682 q^{47} + 114754 q^{48} + 175208 q^{49} + 391142 q^{50} + 18736 q^{51} + 123826 q^{52} - 7269 q^{53} - 16418 q^{54} - 187790 q^{55} - 180760 q^{56} + 208540 q^{57} - 516630 q^{58} - 118496 q^{59} - 176672 q^{60} - 234586 q^{61} - 518632 q^{62} - 267104 q^{63} + 353088 q^{64} + 295923 q^{65} + 201940 q^{66} + 374606 q^{67} + 784334 q^{68} + 251908 q^{69} + 1626418 q^{70} + 1062688 q^{71} + 141394 q^{72} - 943009 q^{73} - 1448740 q^{74} - 936852 q^{75} - 2256516 q^{76} - 1340400 q^{77} - 1437204 q^{78} - 174414 q^{79} - 817770 q^{80} - 140316 q^{81} + 896022 q^{82} + 723942 q^{83} + 1820740 q^{84} + 1688394 q^{85} + 3022422 q^{86} + 1166160 q^{87} + 3359190 q^{88} + 1891032 q^{89} + 2209808 q^{90} + 352542 q^{91} - 363534 q^{92} - 521404 q^{93} - 1422522 q^{94} - 3116154 q^{95} - 3842520 q^{96} - 2089351 q^{97} - 4534652 q^{98} - 1723788 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(261))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
261.6.a \(\chi_{261}(1, \cdot)\) 261.6.a.a 4 1
261.6.a.b 4
261.6.a.c 5
261.6.a.d 7
261.6.a.e 7
261.6.a.f 8
261.6.a.g 12
261.6.a.h 12
261.6.c \(\chi_{261}(28, \cdot)\) 261.6.c.a 6 1
261.6.c.b 12
261.6.c.c 20
261.6.c.d 24
261.6.e \(\chi_{261}(88, \cdot)\) n/a 280 2
261.6.g \(\chi_{261}(17, \cdot)\) 261.6.g.a 100 2
261.6.i \(\chi_{261}(115, \cdot)\) n/a 296 2
261.6.k \(\chi_{261}(82, \cdot)\) n/a 366 6
261.6.l \(\chi_{261}(41, \cdot)\) n/a 592 4
261.6.o \(\chi_{261}(64, \cdot)\) n/a 372 6
261.6.q \(\chi_{261}(7, \cdot)\) n/a 1776 12
261.6.r \(\chi_{261}(8, \cdot)\) n/a 600 12
261.6.u \(\chi_{261}(4, \cdot)\) n/a 1776 12
261.6.x \(\chi_{261}(2, \cdot)\) n/a 3552 24

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(261))\) into lower level spaces

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