Properties

Label 273.8
Level 273
Weight 8
Dimension 13252
Nonzero newspaces 30
Sturm bound 43008
Trace bound 7

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Defining parameters

Level: \( N \) = \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(43008\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(273))\).

Total New Old
Modular forms 19104 13468 5636
Cusp forms 18528 13252 5276
Eisenstein series 576 216 360

Trace form

\( 13252 q + 24 q^{2} - 72 q^{3} - 1428 q^{4} + 1548 q^{5} + 1920 q^{6} - 1876 q^{7} + 5844 q^{8} + 3048 q^{9} + O(q^{10}) \) \( 13252 q + 24 q^{2} - 72 q^{3} - 1428 q^{4} + 1548 q^{5} + 1920 q^{6} - 1876 q^{7} + 5844 q^{8} + 3048 q^{9} - 66864 q^{10} + 17028 q^{11} + 121308 q^{12} + 57830 q^{13} + 56112 q^{14} - 156300 q^{15} - 504724 q^{16} - 273516 q^{17} + 361416 q^{18} + 631316 q^{19} + 356568 q^{20} - 296880 q^{21} - 1840992 q^{22} - 638400 q^{23} + 1275528 q^{24} + 1424440 q^{25} + 2326110 q^{26} + 387060 q^{27} + 487780 q^{28} - 1585476 q^{29} - 5504292 q^{30} - 4205228 q^{31} - 862740 q^{32} + 2025504 q^{33} + 7741032 q^{34} + 3926532 q^{35} - 1009668 q^{36} + 436260 q^{37} + 637716 q^{38} - 7023570 q^{39} - 1820304 q^{40} + 4312716 q^{41} - 4106424 q^{42} - 2880824 q^{43} + 178296 q^{44} + 11894508 q^{45} - 14769480 q^{46} - 6678684 q^{47} - 4507704 q^{48} - 308592 q^{49} + 14133108 q^{50} - 1497708 q^{51} + 40862048 q^{52} + 24302664 q^{53} + 20780052 q^{54} - 11693352 q^{55} - 14010960 q^{56} - 11245224 q^{57} - 29620320 q^{58} - 20091744 q^{59} - 32557788 q^{60} - 29620256 q^{61} - 11741808 q^{62} - 12548004 q^{63} + 68113236 q^{64} + 43218786 q^{65} + 2748468 q^{66} + 10806684 q^{67} + 25834560 q^{68} + 26934876 q^{69} + 39984456 q^{70} - 15551880 q^{71} - 41525688 q^{72} + 9380264 q^{73} + 12420948 q^{74} - 40880940 q^{75} - 133335232 q^{76} - 87378096 q^{77} - 69635856 q^{78} + 3980468 q^{79} + 57281424 q^{80} - 59599788 q^{81} + 224015424 q^{82} + 108688536 q^{83} + 119748228 q^{84} + 6637500 q^{85} - 101200428 q^{86} + 11949624 q^{87} - 190383168 q^{88} - 15175008 q^{89} - 45664560 q^{90} - 154739744 q^{91} - 260434128 q^{92} - 130024704 q^{93} - 133671744 q^{94} - 91176228 q^{95} + 272761452 q^{96} + 268288096 q^{97} + 329760576 q^{98} - 49475232 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(273))\)

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
273.8.a \(\chi_{273}(1, \cdot)\) 273.8.a.a 7 1
273.8.a.b 9
273.8.a.c 10
273.8.a.d 11
273.8.a.e 11
273.8.a.f 12
273.8.a.g 12
273.8.a.h 12
273.8.c \(\chi_{273}(64, \cdot)\) 273.8.c.a 48 1
273.8.c.b 48
273.8.e \(\chi_{273}(209, \cdot)\) n/a 224 1
273.8.g \(\chi_{273}(272, \cdot)\) n/a 256 1
273.8.i \(\chi_{273}(79, \cdot)\) n/a 224 2
273.8.j \(\chi_{273}(100, \cdot)\) n/a 262 2
273.8.k \(\chi_{273}(22, \cdot)\) n/a 200 2
273.8.l \(\chi_{273}(16, \cdot)\) n/a 262 2
273.8.n \(\chi_{273}(8, \cdot)\) n/a 392 2
273.8.p \(\chi_{273}(34, \cdot)\) n/a 264 2
273.8.r \(\chi_{273}(68, \cdot)\) n/a 514 2
273.8.t \(\chi_{273}(4, \cdot)\) n/a 262 2
273.8.u \(\chi_{273}(62, \cdot)\) n/a 516 2
273.8.y \(\chi_{273}(101, \cdot)\) n/a 514 2
273.8.ba \(\chi_{273}(38, \cdot)\) n/a 516 2
273.8.bd \(\chi_{273}(43, \cdot)\) n/a 192 2
273.8.bf \(\chi_{273}(152, \cdot)\) n/a 514 2
273.8.bh \(\chi_{273}(131, \cdot)\) n/a 448 2
273.8.bj \(\chi_{273}(25, \cdot)\) n/a 260 2
273.8.bl \(\chi_{273}(88, \cdot)\) n/a 262 2
273.8.bn \(\chi_{273}(146, \cdot)\) n/a 516 2
273.8.br \(\chi_{273}(17, \cdot)\) n/a 514 2
273.8.bt \(\chi_{273}(136, \cdot)\) n/a 524 4
273.8.bv \(\chi_{273}(2, \cdot)\) n/a 1028 4
273.8.bw \(\chi_{273}(11, \cdot)\) n/a 1028 4
273.8.by \(\chi_{273}(76, \cdot)\) n/a 520 4
273.8.bz \(\chi_{273}(31, \cdot)\) n/a 520 4
273.8.cc \(\chi_{273}(50, \cdot)\) n/a 784 4
273.8.cd \(\chi_{273}(44, \cdot)\) n/a 1032 4
273.8.cg \(\chi_{273}(19, \cdot)\) n/a 524 4

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(273))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(273)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)