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Properties

Label 361.6
Level 361
Weight 6
Dimension 26691
Nonzero newspaces 6
Sturm bound 64980
Trace bound 1

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Defining parameters

Level: \( N \) = \( 361 = 19^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(64980\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(361))\).

Total New Old
Modular forms 27327 27160 167
Cusp forms 26823 26691 132
Eisenstein series 504 469 35

Trace form

\( 26691 q - 153 q^{2} - 153 q^{3} - 153 q^{4} - 153 q^{5} - 153 q^{6} - 153 q^{7} - 153 q^{8} - 153 q^{9} + O(q^{10}) \) \( 26691 q - 153 q^{2} - 153 q^{3} - 153 q^{4} - 153 q^{5} - 153 q^{6} - 153 q^{7} - 153 q^{8} - 153 q^{9} - 153 q^{10} - 153 q^{11} + 3303 q^{12} - 4497 q^{13} - 8073 q^{14} - 3717 q^{15} + 5607 q^{16} + 4149 q^{17} + 17361 q^{18} + 6243 q^{19} + 12375 q^{20} - 2043 q^{21} - 17217 q^{22} - 10431 q^{23} - 51993 q^{24} - 23517 q^{25} - 8073 q^{26} + 64665 q^{27} + 86277 q^{28} - 22869 q^{29} - 139887 q^{30} - 39429 q^{31} - 67743 q^{32} - 25965 q^{33} + 28557 q^{34} + 58959 q^{35} + 214443 q^{36} + 49149 q^{37} + 83691 q^{38} + 115155 q^{39} + 76149 q^{40} - 1269 q^{41} - 137133 q^{42} - 56427 q^{43} + 5913 q^{44} - 254331 q^{45} - 346491 q^{46} - 211383 q^{47} - 415323 q^{48} - 30111 q^{49} + 77265 q^{50} + 144459 q^{51} + 61095 q^{52} + 104895 q^{53} + 250893 q^{54} + 205839 q^{55} + 677241 q^{56} + 138393 q^{57} + 192951 q^{58} + 177057 q^{59} + 709137 q^{60} + 359499 q^{61} - 80811 q^{62} - 449361 q^{63} - 1188105 q^{64} - 1020663 q^{65} - 1521513 q^{66} - 834351 q^{67} - 880515 q^{68} - 290727 q^{69} + 214479 q^{70} + 553869 q^{71} + 1747845 q^{72} + 877179 q^{73} + 757143 q^{74} + 944865 q^{75} + 499248 q^{76} + 1311921 q^{77} + 1574595 q^{78} + 581763 q^{79} - 74313 q^{80} - 572535 q^{81} - 1364391 q^{82} - 820971 q^{83} - 3226977 q^{84} - 1686321 q^{85} - 1518399 q^{86} - 1742265 q^{87} - 1280457 q^{88} - 546579 q^{89} + 490977 q^{90} + 802191 q^{91} + 2161881 q^{92} + 2599011 q^{93} + 3961809 q^{94} + 1015641 q^{95} + 3695463 q^{96} + 403209 q^{97} - 430047 q^{98} - 827379 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(361))\)

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
361.6.a \(\chi_{361}(1, \cdot)\) 361.6.a.a 1 1
361.6.a.b 1
361.6.a.c 1
361.6.a.d 2
361.6.a.e 4
361.6.a.f 6
361.6.a.g 8
361.6.a.h 8
361.6.a.i 16
361.6.a.j 16
361.6.a.k 21
361.6.a.l 21
361.6.a.m 28
361.6.c \(\chi_{361}(68, \cdot)\) n/a 266 2
361.6.e \(\chi_{361}(28, \cdot)\) n/a 804 6
361.6.g \(\chi_{361}(20, \cdot)\) n/a 2844 18
361.6.i \(\chi_{361}(7, \cdot)\) n/a 5688 36
361.6.k \(\chi_{361}(4, \cdot)\) n/a 16956 108

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(361))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(361)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 1}\)