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Properties

Label 578.2
Level 578
Weight 2
Dimension 3445
Nonzero newspaces 8
Newform subspaces 40
Sturm bound 41616
Trace bound 2

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Defining parameters

Level: \( N \) = \( 578 = 2 \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 40 \)
Sturm bound: \(41616\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(578))\).

Total New Old
Modular forms 10804 3445 7359
Cusp forms 10005 3445 6560
Eisenstein series 799 0 799

Trace form

\( 3445 q + q^{2} + 4 q^{3} + q^{4} + 6 q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + O(q^{10}) \) \( 3445 q + q^{2} + 4 q^{3} + q^{4} + 6 q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} - 2 q^{10} - 20 q^{11} - 12 q^{12} - 18 q^{13} - 24 q^{14} - 72 q^{15} - 7 q^{16} - 16 q^{17} - 51 q^{18} - 12 q^{19} - 2 q^{20} - 64 q^{21} - 20 q^{22} - 8 q^{23} - 12 q^{24} - 41 q^{25} + 6 q^{26} - 8 q^{27} + 8 q^{28} - 10 q^{29} + 24 q^{30} - 32 q^{31} + q^{32} - 16 q^{33} - 16 q^{35} + 13 q^{36} - 26 q^{37} + 4 q^{38} - 72 q^{39} + 6 q^{40} - 94 q^{41} - 64 q^{42} - 68 q^{43} - 52 q^{44} - 90 q^{45} - 40 q^{46} - 112 q^{47} + 4 q^{48} - 71 q^{49} - 81 q^{50} - 64 q^{51} - 50 q^{52} - 82 q^{53} - 72 q^{54} - 88 q^{55} + 8 q^{56} - 96 q^{57} - 34 q^{58} - 100 q^{59} - 40 q^{60} - 34 q^{61} - 64 q^{62} - 88 q^{63} + q^{64} + 12 q^{65} + 32 q^{66} + 36 q^{67} - 4 q^{68} - 32 q^{69} - 16 q^{70} - 24 q^{71} - 27 q^{72} - 94 q^{73} - 34 q^{74} - 100 q^{75} + 20 q^{76} - 64 q^{77} - 72 q^{78} - 80 q^{79} - 26 q^{80} - 87 q^{81} - 94 q^{82} - 60 q^{83} - 32 q^{84} - 132 q^{85} - 20 q^{86} - 168 q^{87} - 52 q^{88} - 102 q^{89} - 58 q^{90} - 208 q^{91} - 8 q^{92} - 128 q^{93} - 80 q^{94} - 168 q^{95} + 4 q^{96} - 94 q^{97} - 15 q^{98} - 212 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)

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
578.2.a \(\chi_{578}(1, \cdot)\) 578.2.a.a 1 1
578.2.a.b 2
578.2.a.c 2
578.2.a.d 2
578.2.a.e 3
578.2.a.f 3
578.2.a.g 3
578.2.a.h 3
578.2.a.i 4
578.2.b \(\chi_{578}(577, \cdot)\) 578.2.b.a 2 1
578.2.b.b 2
578.2.b.c 2
578.2.b.d 4
578.2.b.e 6
578.2.b.f 6
578.2.c \(\chi_{578}(251, \cdot)\) 578.2.c.a 2 2
578.2.c.b 2
578.2.c.c 2
578.2.c.d 2
578.2.c.e 4
578.2.c.f 8
578.2.c.g 12
578.2.c.h 12
578.2.d \(\chi_{578}(155, \cdot)\) 578.2.d.a 4 4
578.2.d.b 4
578.2.d.c 4
578.2.d.d 8
578.2.d.e 8
578.2.d.f 8
578.2.d.g 8
578.2.d.h 24
578.2.d.i 24
578.2.f \(\chi_{578}(35, \cdot)\) 578.2.f.a 192 16
578.2.f.b 224
578.2.g \(\chi_{578}(33, \cdot)\) 578.2.g.a 192 16
578.2.g.b 224
578.2.h \(\chi_{578}(13, \cdot)\) 578.2.h.a 416 32
578.2.h.b 416
578.2.i \(\chi_{578}(9, \cdot)\) 578.2.i.a 768 64
578.2.i.b 832

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(578))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(578)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 2}\)