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Properties

Label 464.3
Level 464
Weight 3
Dimension 7420
Nonzero newspaces 14
Sturm bound 40320
Trace bound 9

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Defining parameters

Level: \( N \) = \( 464 = 2^{4} \cdot 29 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(40320\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(464))\).

Total New Old
Modular forms 13832 7664 6168
Cusp forms 13048 7420 5628
Eisenstein series 784 244 540

Trace form

\( 7420 q - 52 q^{2} - 38 q^{3} - 40 q^{4} - 54 q^{5} - 40 q^{6} - 34 q^{7} - 64 q^{8} - 32 q^{9} + O(q^{10}) \) \( 7420 q - 52 q^{2} - 38 q^{3} - 40 q^{4} - 54 q^{5} - 40 q^{6} - 34 q^{7} - 64 q^{8} - 32 q^{9} - 128 q^{10} - 6 q^{11} - 160 q^{12} - 86 q^{13} - 80 q^{14} - 42 q^{15} + 24 q^{16} - 58 q^{17} + 92 q^{18} - 102 q^{19} + 112 q^{20} - 30 q^{21} + 48 q^{22} - 162 q^{23} - 152 q^{24} - 36 q^{25} - 248 q^{26} - 170 q^{27} - 168 q^{28} - 94 q^{29} - 216 q^{30} - 42 q^{31} - 72 q^{32} - 118 q^{33} + 96 q^{34} + 158 q^{35} + 48 q^{36} - 22 q^{37} - 136 q^{38} + 350 q^{39} - 136 q^{40} - 50 q^{41} - 8 q^{42} + 186 q^{43} - 96 q^{44} - 94 q^{45} - 112 q^{46} - 42 q^{47} - 8 q^{48} - 132 q^{49} - 148 q^{50} - 354 q^{51} - 256 q^{52} - 406 q^{53} - 120 q^{54} - 546 q^{55} + 280 q^{56} + 120 q^{58} - 496 q^{59} + 264 q^{60} - 86 q^{61} + 232 q^{62} - 42 q^{63} - 184 q^{64} - 30 q^{65} - 448 q^{66} + 410 q^{67} - 280 q^{68} + 162 q^{69} - 24 q^{70} + 478 q^{71} - 160 q^{72} + 206 q^{73} + 128 q^{74} + 434 q^{75} + 320 q^{76} + 354 q^{77} + 112 q^{78} - 42 q^{79} - 520 q^{80} - 460 q^{81} - 664 q^{82} - 678 q^{83} - 520 q^{84} - 6 q^{85} - 592 q^{86} - 486 q^{87} - 96 q^{88} + 142 q^{89} + 264 q^{90} - 418 q^{91} + 280 q^{92} - 6 q^{93} - 152 q^{94} - 42 q^{95} + 104 q^{96} + 630 q^{97} - 76 q^{98} + 3098 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(464))\)

We only show spaces with odd 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
464.3.b \(\chi_{464}(231, \cdot)\) None 0 1
464.3.d \(\chi_{464}(175, \cdot)\) 464.3.d.a 8 1
464.3.d.b 20
464.3.f \(\chi_{464}(407, \cdot)\) None 0 1
464.3.h \(\chi_{464}(463, \cdot)\) 464.3.h.a 4 1
464.3.h.b 6
464.3.h.c 20
464.3.i \(\chi_{464}(133, \cdot)\) n/a 236 2
464.3.l \(\chi_{464}(17, \cdot)\) 464.3.l.a 4 2
464.3.l.b 6
464.3.l.c 8
464.3.l.d 10
464.3.l.e 14
464.3.l.f 16
464.3.o \(\chi_{464}(59, \cdot)\) n/a 224 2
464.3.p \(\chi_{464}(115, \cdot)\) n/a 236 2
464.3.r \(\chi_{464}(41, \cdot)\) None 0 2
464.3.s \(\chi_{464}(365, \cdot)\) n/a 236 2
464.3.v \(\chi_{464}(63, \cdot)\) n/a 180 6
464.3.x \(\chi_{464}(7, \cdot)\) None 0 6
464.3.z \(\chi_{464}(111, \cdot)\) n/a 180 6
464.3.bb \(\chi_{464}(71, \cdot)\) None 0 6
464.3.bd \(\chi_{464}(37, \cdot)\) n/a 1416 12
464.3.be \(\chi_{464}(73, \cdot)\) None 0 12
464.3.bg \(\chi_{464}(35, \cdot)\) n/a 1416 12
464.3.bh \(\chi_{464}(83, \cdot)\) n/a 1416 12
464.3.bk \(\chi_{464}(97, \cdot)\) n/a 348 12
464.3.bn \(\chi_{464}(21, \cdot)\) n/a 1416 12

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(464))\) into lower level spaces

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