Properties

Label 342.3
Level 342
Weight 3
Dimension 1698
Nonzero newspaces 16
Newform subspaces 29
Sturm bound 19440
Trace bound 4

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Defining parameters

Level: \( N \) = \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 29 \)
Sturm bound: \(19440\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(342))\).

Total New Old
Modular forms 6768 1698 5070
Cusp forms 6192 1698 4494
Eisenstein series 576 0 576

Trace form

\( 1698q + 36q^{5} + 24q^{6} + 12q^{7} - 24q^{9} + O(q^{10}) \) \( 1698q + 36q^{5} + 24q^{6} + 12q^{7} - 24q^{9} - 24q^{10} - 36q^{11} - 24q^{12} - 132q^{13} - 144q^{14} - 36q^{15} - 18q^{17} + 48q^{18} + 114q^{19} + 108q^{20} + 84q^{21} + 228q^{22} + 54q^{23} + 216q^{25} + 144q^{26} + 12q^{28} - 180q^{29} - 144q^{30} - 360q^{31} - 108q^{33} - 120q^{34} - 72q^{35} - 24q^{36} - 120q^{37} + 72q^{38} + 204q^{39} + 48q^{40} + 324q^{41} + 96q^{42} + 702q^{43} + 324q^{44} + 1296q^{45} + 1032q^{46} + 1530q^{47} + 96q^{48} + 1254q^{49} + 1296q^{50} + 1044q^{51} + 96q^{52} + 648q^{53} + 144q^{54} + 144q^{55} - 144q^{56} - 324q^{57} - 240q^{58} - 1062q^{59} - 216q^{60} - 1488q^{61} - 972q^{62} - 1452q^{63} - 48q^{64} - 2790q^{65} - 1296q^{66} - 1494q^{67} - 468q^{68} - 1440q^{69} - 1200q^{70} - 2502q^{71} - 96q^{72} + 120q^{73} - 144q^{74} + 24q^{75} - 24q^{76} - 90q^{77} - 288q^{78} - 96q^{79} + 504q^{81} - 456q^{82} + 306q^{83} + 288q^{84} - 648q^{85} - 72q^{86} + 108q^{87} - 240q^{88} - 18q^{89} - 528q^{91} - 144q^{92} - 444q^{93} - 648q^{94} + 1818q^{95} - 96q^{96} + 1158q^{97} + 288q^{98} + 1512q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(342))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
342.3.c \(\chi_{342}(305, \cdot)\) 342.3.c.a 4 1
342.3.c.b 8
342.3.d \(\chi_{342}(37, \cdot)\) 342.3.d.a 2 1
342.3.d.b 8
342.3.d.c 8
342.3.i \(\chi_{342}(11, \cdot)\) 342.3.i.a 80 2
342.3.k \(\chi_{342}(103, \cdot)\) 342.3.k.a 80 2
342.3.l \(\chi_{342}(151, \cdot)\) 342.3.l.a 80 2
342.3.m \(\chi_{342}(145, \cdot)\) 342.3.m.a 4 2
342.3.m.b 8
342.3.m.c 8
342.3.m.d 16
342.3.o \(\chi_{342}(77, \cdot)\) 342.3.o.a 72 2
342.3.q \(\chi_{342}(83, \cdot)\) 342.3.q.a 80 2
342.3.r \(\chi_{342}(125, \cdot)\) 342.3.r.a 4 2
342.3.r.b 4
342.3.r.c 12
342.3.r.d 12
342.3.t \(\chi_{342}(31, \cdot)\) 342.3.t.a 80 2
342.3.y \(\chi_{342}(5, \cdot)\) 342.3.y.a 240 6
342.3.z \(\chi_{342}(91, \cdot)\) 342.3.z.a 12 6
342.3.z.b 24
342.3.z.c 24
342.3.z.d 36
342.3.ba \(\chi_{342}(17, \cdot)\) 342.3.ba.a 36 6
342.3.ba.b 36
342.3.bc \(\chi_{342}(193, \cdot)\) 342.3.bc.a 240 6
342.3.bd \(\chi_{342}(13, \cdot)\) 342.3.bd.a 240 6
342.3.be \(\chi_{342}(23, \cdot)\) 342.3.be.a 240 6

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(342))\) into lower level spaces

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