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Properties

Label 342.5
Level 342
Weight 5
Dimension 3404
Nonzero newspaces 16
Sturm bound 32400
Trace bound 4

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Defining parameters

Level: \( N \) = \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(32400\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(342))\).

Total New Old
Modular forms 13248 3404 9844
Cusp forms 12672 3404 9268
Eisenstein series 576 0 576

Trace form

\( 3404 q - 12 q^{3} - 64 q^{4} - 36 q^{5} - 96 q^{6} + 52 q^{7} + 156 q^{9} + O(q^{10}) \) \( 3404 q - 12 q^{3} - 64 q^{4} - 36 q^{5} - 96 q^{6} + 52 q^{7} + 156 q^{9} + 1440 q^{11} + 288 q^{12} + 100 q^{13} + 288 q^{14} - 2268 q^{15} + 512 q^{16} + 594 q^{17} + 768 q^{18} - 1654 q^{19} - 1584 q^{20} - 876 q^{21} - 3696 q^{22} - 4446 q^{23} - 768 q^{24} - 1840 q^{25} + 1728 q^{26} + 2592 q^{27} + 3472 q^{28} + 2844 q^{29} + 6912 q^{30} + 5764 q^{31} + 6768 q^{33} + 192 q^{34} + 4752 q^{35} - 2112 q^{36} + 64 q^{37} - 6768 q^{38} - 10548 q^{39} - 4680 q^{41} - 5184 q^{42} + 8758 q^{43} + 18144 q^{44} + 30024 q^{45} + 4416 q^{46} - 22302 q^{47} - 1536 q^{48} - 38166 q^{49} - 51840 q^{50} - 45288 q^{51} - 6176 q^{52} - 62856 q^{53} - 36576 q^{54} - 15552 q^{55} - 4608 q^{56} + 9438 q^{57} + 28992 q^{58} + 70074 q^{59} + 16992 q^{60} + 107500 q^{61} + 85536 q^{62} + 90924 q^{63} + 17408 q^{64} + 169578 q^{65} + 85824 q^{66} + 23170 q^{67} + 19584 q^{68} - 31536 q^{69} - 96768 q^{70} - 192618 q^{71} - 43008 q^{72} - 77522 q^{73} - 30528 q^{74} - 33180 q^{75} - 400 q^{76} - 115578 q^{77} - 48192 q^{78} - 47936 q^{79} + 42300 q^{81} + 6336 q^{82} + 19710 q^{83} + 19200 q^{84} + 89856 q^{85} + 56160 q^{86} - 20340 q^{87} + 5376 q^{88} + 45846 q^{89} - 5184 q^{90} + 157520 q^{91} - 7488 q^{92} + 21852 q^{93} - 1344 q^{94} + 229410 q^{95} + 14494 q^{97} - 51840 q^{98} + 41148 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(342))\)

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
342.5.c \(\chi_{342}(305, \cdot)\) 342.5.c.a 12 1
342.5.c.b 12
342.5.d \(\chi_{342}(37, \cdot)\) 342.5.d.a 8 1
342.5.d.b 12
342.5.d.c 12
342.5.i \(\chi_{342}(11, \cdot)\) n/a 160 2
342.5.k \(\chi_{342}(103, \cdot)\) n/a 160 2
342.5.l \(\chi_{342}(151, \cdot)\) n/a 160 2
342.5.m \(\chi_{342}(145, \cdot)\) 342.5.m.a 12 2
342.5.m.b 12
342.5.m.c 16
342.5.m.d 24
342.5.o \(\chi_{342}(77, \cdot)\) n/a 144 2
342.5.q \(\chi_{342}(83, \cdot)\) n/a 160 2
342.5.r \(\chi_{342}(125, \cdot)\) 342.5.r.a 24 2
342.5.r.b 24
342.5.t \(\chi_{342}(31, \cdot)\) n/a 160 2
342.5.y \(\chi_{342}(5, \cdot)\) n/a 480 6
342.5.z \(\chi_{342}(91, \cdot)\) n/a 204 6
342.5.ba \(\chi_{342}(17, \cdot)\) n/a 168 6
342.5.bc \(\chi_{342}(193, \cdot)\) n/a 480 6
342.5.bd \(\chi_{342}(13, \cdot)\) n/a 480 6
342.5.be \(\chi_{342}(23, \cdot)\) n/a 480 6

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(342))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(342)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 1}\)