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Properties

Label 58.8
Level 58
Weight 8
Dimension 243
Nonzero newspaces 4
Newform subspaces 8
Sturm bound 1680
Trace bound 1

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Defining parameters

Level: \( N \) = \( 58 = 2 \cdot 29 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 8 \)
Sturm bound: \(1680\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(58))\).

Total New Old
Modular forms 763 243 520
Cusp forms 707 243 464
Eisenstein series 56 0 56

Trace form

\( 243 q + 16 q^{2} - 24 q^{3} - 128 q^{4} + 420 q^{5} + 192 q^{6} - 2032 q^{7} + 1024 q^{8} + 4086 q^{9} + O(q^{10}) \) \( 243 q + 16 q^{2} - 24 q^{3} - 128 q^{4} + 420 q^{5} + 192 q^{6} - 2032 q^{7} + 1024 q^{8} + 4086 q^{9} - 3360 q^{10} - 2184 q^{11} - 1536 q^{12} - 2764 q^{13} + 16256 q^{14} + 5040 q^{15} - 8192 q^{16} - 29412 q^{17} - 32688 q^{18} + 79880 q^{19} + 13888 q^{20} - 811912 q^{21} - 38752 q^{22} + 168700 q^{23} + 428032 q^{24} + 556874 q^{25} - 95768 q^{26} - 1195692 q^{27} - 130048 q^{28} - 988702 q^{29} - 690144 q^{30} + 120408 q^{31} + 65536 q^{32} + 3326484 q^{33} + 1520776 q^{34} + 1252664 q^{35} - 414080 q^{36} - 2215616 q^{37} - 3116256 q^{38} - 2189560 q^{39} + 885248 q^{40} - 21684 q^{41} + 195072 q^{42} + 1261496 q^{43} - 139776 q^{44} - 1597995 q^{45} + 1099392 q^{46} - 4541156 q^{47} - 98304 q^{48} + 3108278 q^{49} - 544400 q^{50} + 7786152 q^{51} - 176896 q^{52} + 6581745 q^{53} - 812160 q^{54} - 10529792 q^{55} + 1040384 q^{56} - 9412248 q^{57} - 820560 q^{58} - 8823068 q^{59} + 322560 q^{60} + 1494652 q^{61} + 3640832 q^{62} + 31666752 q^{63} - 524288 q^{64} + 18139737 q^{65} + 209664 q^{66} + 2639680 q^{67} - 1882368 q^{68} - 23093784 q^{69} + 25230688 q^{70} - 23470160 q^{71} - 2092032 q^{72} - 11777511 q^{73} - 27696448 q^{74} - 7154860 q^{75} + 17803264 q^{76} + 58039436 q^{77} + 59223040 q^{78} + 35753464 q^{79} + 1720320 q^{80} + 40488974 q^{81} - 203296 q^{82} - 37404488 q^{83} - 37681920 q^{84} - 89784912 q^{85} - 99139808 q^{86} - 84662380 q^{87} + 1118208 q^{88} - 19854760 q^{89} - 1886080 q^{90} + 34123048 q^{91} + 33207552 q^{92} + 77377648 q^{93} + 57932480 q^{94} + 194623184 q^{95} + 786432 q^{96} + 18957189 q^{97} + 23724304 q^{98} - 131981780 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(58))\)

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
58.8.a \(\chi_{58}(1, \cdot)\) 58.8.a.a 3 1
58.8.a.b 3
58.8.a.c 4
58.8.a.d 5
58.8.b \(\chi_{58}(57, \cdot)\) 58.8.b.a 18 1
58.8.d \(\chi_{58}(7, \cdot)\) 58.8.d.a 48 6
58.8.d.b 54
58.8.e \(\chi_{58}(5, \cdot)\) 58.8.e.a 108 6

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(58))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(58)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)