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Properties

Label 594.2
Level 594
Weight 2
Dimension 2516
Nonzero newspaces 12
Newform subspaces 53
Sturm bound 38880
Trace bound 8

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Defining parameters

Level: \( N \) = \( 594 = 2 \cdot 3^{3} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 53 \)
Sturm bound: \(38880\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(594))\).

Total New Old
Modular forms 10320 2516 7804
Cusp forms 9121 2516 6605
Eisenstein series 1199 0 1199

Trace form

\( 2516 q - 2 q^{2} - 2 q^{4} + 12 q^{5} + 12 q^{6} + 8 q^{7} + 10 q^{8} + 24 q^{9} + O(q^{10}) \) \( 2516 q - 2 q^{2} - 2 q^{4} + 12 q^{5} + 12 q^{6} + 8 q^{7} + 10 q^{8} + 24 q^{9} + 12 q^{10} + 18 q^{11} + 6 q^{12} + 20 q^{13} + 8 q^{14} + 36 q^{15} - 2 q^{16} + 12 q^{17} - 12 q^{18} - 4 q^{19} - 24 q^{20} - 48 q^{21} - 16 q^{23} + 50 q^{25} - 24 q^{26} - 54 q^{27} + 16 q^{28} - 12 q^{29} - 72 q^{30} + 48 q^{31} + 8 q^{32} - 27 q^{33} + 52 q^{34} + 88 q^{35} - 12 q^{36} + 48 q^{37} + 86 q^{38} + 84 q^{39} + 32 q^{40} + 72 q^{41} + 48 q^{42} + 96 q^{43} + 10 q^{44} + 12 q^{47} + 12 q^{48} + 54 q^{49} + 82 q^{50} + 20 q^{52} + 136 q^{53} + 72 q^{54} + 58 q^{55} + 8 q^{56} + 18 q^{57} + 36 q^{58} + 52 q^{59} + 36 q^{60} + 60 q^{61} + 32 q^{62} + 12 q^{63} + 10 q^{64} + 68 q^{65} - 20 q^{67} + 30 q^{68} - 36 q^{69} - 84 q^{70} - 16 q^{71} - 48 q^{72} + 60 q^{73} - 52 q^{74} - 24 q^{75} - 46 q^{76} + 44 q^{77} - 72 q^{78} - 144 q^{79} - 24 q^{80} - 120 q^{81} - 120 q^{82} - 314 q^{83} - 120 q^{84} - 464 q^{85} - 402 q^{86} - 372 q^{87} - 27 q^{88} - 470 q^{89} - 336 q^{90} - 236 q^{91} - 300 q^{92} - 288 q^{93} - 380 q^{94} - 812 q^{95} - 12 q^{96} - 360 q^{97} - 432 q^{98} - 444 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(594))\)

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
594.2.a \(\chi_{594}(1, \cdot)\) 594.2.a.a 1 1
594.2.a.b 1
594.2.a.c 1
594.2.a.d 1
594.2.a.e 1
594.2.a.f 1
594.2.a.g 1
594.2.a.h 1
594.2.a.i 2
594.2.a.j 2
594.2.b \(\chi_{594}(593, \cdot)\) 594.2.b.a 4 1
594.2.b.b 4
594.2.b.c 4
594.2.b.d 4
594.2.e \(\chi_{594}(199, \cdot)\) 594.2.e.a 2 2
594.2.e.b 2
594.2.e.c 4
594.2.e.d 6
594.2.e.e 6
594.2.f \(\chi_{594}(163, \cdot)\) 594.2.f.a 4 4
594.2.f.b 4
594.2.f.c 4
594.2.f.d 4
594.2.f.e 4
594.2.f.f 4
594.2.f.g 4
594.2.f.h 4
594.2.f.i 4
594.2.f.j 4
594.2.f.k 12
594.2.f.l 12
594.2.i \(\chi_{594}(197, \cdot)\) 594.2.i.a 12 2
594.2.i.b 12
594.2.j \(\chi_{594}(67, \cdot)\) 594.2.j.a 6 6
594.2.j.b 12
594.2.j.c 30
594.2.j.d 42
594.2.j.e 42
594.2.j.f 48
594.2.m \(\chi_{594}(107, \cdot)\) 594.2.m.a 16 4
594.2.m.b 16
594.2.m.c 16
594.2.m.d 16
594.2.n \(\chi_{594}(37, \cdot)\) 594.2.n.a 40 8
594.2.n.b 56
594.2.o \(\chi_{594}(65, \cdot)\) 594.2.o.a 108 6
594.2.o.b 108
594.2.r \(\chi_{594}(17, \cdot)\) 594.2.r.a 48 8
594.2.r.b 48
594.2.u \(\chi_{594}(25, \cdot)\) 594.2.u.a 408 24
594.2.u.b 456
594.2.x \(\chi_{594}(29, \cdot)\) 594.2.x.a 432 24
594.2.x.b 432

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(594))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(594)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 2}\)