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Properties

Label 464.8
Level 464
Weight 8
Dimension 26276
Nonzero newspaces 14
Sturm bound 107520
Trace bound 3

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Defining parameters

Level: \( N \) = \( 464 = 2^{4} \cdot 29 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(107520\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(464))\).

Total New Old
Modular forms 47432 26518 20914
Cusp forms 46648 26276 20372
Eisenstein series 784 242 542

Trace form

\( 26276 q - 52 q^{2} - 94 q^{3} + 312 q^{4} - 342 q^{5} + 296 q^{6} - 1370 q^{7} + 1952 q^{8} - 5164 q^{9} + O(q^{10}) \) \( 26276 q - 52 q^{2} - 94 q^{3} + 312 q^{4} - 342 q^{5} + 296 q^{6} - 1370 q^{7} + 1952 q^{8} - 5164 q^{9} - 26000 q^{10} - 11638 q^{11} + 54656 q^{12} + 6490 q^{13} - 44592 q^{14} + 100542 q^{15} - 26728 q^{16} + 25310 q^{17} + 58636 q^{18} - 203790 q^{19} - 92464 q^{20} - 2094 q^{21} + 88640 q^{22} + 303942 q^{23} + 118376 q^{24} - 2712 q^{25} + 71864 q^{26} - 299338 q^{27} - 440680 q^{28} - 68446 q^{29} - 55384 q^{30} + 161846 q^{31} + 497208 q^{32} - 171926 q^{33} - 1849376 q^{34} - 900610 q^{35} + 2030960 q^{36} - 208710 q^{37} + 10888 q^{38} + 2382214 q^{39} + 2243896 q^{40} + 334294 q^{41} - 249256 q^{42} - 2360326 q^{43} + 1517184 q^{44} - 147502 q^{45} - 4671376 q^{46} + 4302358 q^{47} - 8282632 q^{48} + 2758576 q^{49} + 1574332 q^{50} - 4424674 q^{51} - 820704 q^{52} - 3046022 q^{53} + 14808968 q^{54} - 2765786 q^{55} + 8186264 q^{56} + 2133252 q^{57} + 1860656 q^{58} + 11284368 q^{59} - 10294712 q^{60} - 8220966 q^{61} - 12548248 q^{62} - 24567714 q^{63} - 20904504 q^{64} - 3594974 q^{65} - 21875680 q^{66} + 26127986 q^{67} + 14807464 q^{68} + 21510578 q^{69} + 44281544 q^{70} - 13347546 q^{71} + 50587840 q^{72} + 12741782 q^{73} + 26354032 q^{74} + 8149794 q^{75} - 35628576 q^{76} - 27474990 q^{77} - 75987888 q^{78} + 9891958 q^{79} - 80094600 q^{80} - 5298456 q^{81} - 45716536 q^{82} - 11615294 q^{83} + 60319352 q^{84} + 3584554 q^{85} + 108258880 q^{86} - 4209042 q^{87} + 118432672 q^{88} + 13637110 q^{89} + 67030552 q^{90} - 7514450 q^{91} - 43621928 q^{92} - 5373350 q^{93} - 154392280 q^{94} + 21190302 q^{95} - 233880984 q^{96} - 53824202 q^{97} - 43647788 q^{98} + 200200906 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(464))\)

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
464.8.a \(\chi_{464}(1, \cdot)\) 464.8.a.a 3 1
464.8.a.b 3
464.8.a.c 4
464.8.a.d 5
464.8.a.e 7
464.8.a.f 7
464.8.a.g 10
464.8.a.h 10
464.8.a.i 11
464.8.a.j 12
464.8.a.k 13
464.8.a.l 13
464.8.c \(\chi_{464}(233, \cdot)\) None 0 1
464.8.e \(\chi_{464}(289, \cdot)\) n/a 104 1
464.8.g \(\chi_{464}(57, \cdot)\) None 0 1
464.8.j \(\chi_{464}(307, \cdot)\) n/a 836 2
464.8.k \(\chi_{464}(191, \cdot)\) n/a 210 2
464.8.m \(\chi_{464}(173, \cdot)\) n/a 836 2
464.8.n \(\chi_{464}(117, \cdot)\) n/a 784 2
464.8.q \(\chi_{464}(215, \cdot)\) None 0 2
464.8.t \(\chi_{464}(75, \cdot)\) n/a 836 2
464.8.u \(\chi_{464}(49, \cdot)\) n/a 624 6
464.8.w \(\chi_{464}(9, \cdot)\) None 0 6
464.8.y \(\chi_{464}(33, \cdot)\) n/a 624 6
464.8.ba \(\chi_{464}(25, \cdot)\) None 0 6
464.8.bc \(\chi_{464}(11, \cdot)\) n/a 5016 12
464.8.bf \(\chi_{464}(39, \cdot)\) None 0 12
464.8.bi \(\chi_{464}(45, \cdot)\) n/a 5016 12
464.8.bj \(\chi_{464}(5, \cdot)\) n/a 5016 12
464.8.bl \(\chi_{464}(15, \cdot)\) n/a 1260 12
464.8.bm \(\chi_{464}(3, \cdot)\) n/a 5016 12

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(464))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(464)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(464))\)\(^{\oplus 1}\)