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Properties

Label 1608.2
Level 1608
Weight 2
Dimension 30020
Nonzero newspaces 24
Sturm bound 287232
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1608 = 2^{3} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(287232\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1608))\).

Total New Old
Modular forms 73392 30540 42852
Cusp forms 70225 30020 40205
Eisenstein series 3167 520 2647

Trace form

\( 30020 q + 4 q^{2} - 60 q^{3} - 124 q^{4} + 4 q^{5} - 70 q^{6} - 124 q^{7} - 8 q^{8} - 126 q^{9} + O(q^{10}) \) \( 30020 q + 4 q^{2} - 60 q^{3} - 124 q^{4} + 4 q^{5} - 70 q^{6} - 124 q^{7} - 8 q^{8} - 126 q^{9} - 140 q^{10} - 8 q^{11} - 82 q^{12} + 4 q^{13} - 8 q^{14} - 78 q^{15} - 132 q^{16} + 4 q^{17} - 54 q^{18} - 132 q^{19} + 16 q^{20} - 116 q^{22} - 42 q^{24} - 246 q^{25} + 16 q^{26} - 84 q^{27} - 132 q^{28} - 12 q^{29} - 58 q^{30} - 156 q^{31} - 16 q^{32} - 140 q^{33} - 172 q^{34} - 74 q^{36} - 12 q^{37} - 16 q^{38} - 54 q^{39} - 148 q^{40} + 4 q^{41} - 74 q^{42} - 100 q^{43} + 4 q^{45} - 116 q^{46} + 48 q^{47} - 50 q^{48} - 266 q^{49} + 4 q^{50} - 30 q^{51} - 164 q^{52} + 4 q^{53} - 78 q^{54} - 116 q^{55} + 16 q^{56} - 148 q^{57} - 108 q^{58} - 8 q^{59} - 66 q^{60} + 4 q^{61} + 8 q^{62} - 74 q^{63} - 100 q^{64} - 40 q^{65} - 82 q^{66} - 156 q^{67} - 16 q^{69} - 116 q^{70} - 64 q^{71} - 90 q^{72} - 268 q^{73} - 32 q^{74} - 88 q^{75} - 84 q^{76} - 82 q^{78} - 156 q^{79} - 110 q^{81} - 60 q^{82} + 8 q^{83} - 50 q^{84} + 8 q^{85} + 16 q^{86} - 30 q^{87} - 164 q^{88} + 52 q^{89} - 58 q^{90} - 132 q^{91} + 16 q^{93} - 180 q^{94} + 16 q^{95} - 114 q^{96} - 220 q^{97} - 12 q^{98} - 42 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1608))\)

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
1608.2.a \(\chi_{1608}(1, \cdot)\) 1608.2.a.a 1 1
1608.2.a.b 1
1608.2.a.c 2
1608.2.a.d 3
1608.2.a.e 3
1608.2.a.f 3
1608.2.a.g 4
1608.2.a.h 4
1608.2.a.i 5
1608.2.a.j 6
1608.2.c \(\chi_{1608}(1205, \cdot)\) n/a 268 1
1608.2.e \(\chi_{1608}(671, \cdot)\) None 0 1
1608.2.f \(\chi_{1608}(805, \cdot)\) n/a 132 1
1608.2.h \(\chi_{1608}(535, \cdot)\) None 0 1
1608.2.j \(\chi_{1608}(1475, \cdot)\) n/a 264 1
1608.2.l \(\chi_{1608}(401, \cdot)\) 1608.2.l.a 34 1
1608.2.l.b 34
1608.2.o \(\chi_{1608}(1339, \cdot)\) n/a 136 1
1608.2.q \(\chi_{1608}(841, \cdot)\) 1608.2.q.a 2 2
1608.2.q.b 6
1608.2.q.c 10
1608.2.q.d 16
1608.2.q.e 16
1608.2.q.f 18
1608.2.s \(\chi_{1608}(775, \cdot)\) None 0 2
1608.2.u \(\chi_{1608}(37, \cdot)\) n/a 272 2
1608.2.v \(\chi_{1608}(431, \cdot)\) None 0 2
1608.2.x \(\chi_{1608}(365, \cdot)\) n/a 536 2
1608.2.ba \(\chi_{1608}(499, \cdot)\) n/a 272 2
1608.2.bd \(\chi_{1608}(641, \cdot)\) n/a 136 2
1608.2.bf \(\chi_{1608}(707, \cdot)\) n/a 536 2
1608.2.bg \(\chi_{1608}(25, \cdot)\) n/a 340 10
1608.2.bi \(\chi_{1608}(43, \cdot)\) n/a 1360 10
1608.2.bl \(\chi_{1608}(137, \cdot)\) n/a 680 10
1608.2.bn \(\chi_{1608}(59, \cdot)\) n/a 2680 10
1608.2.bp \(\chi_{1608}(271, \cdot)\) None 0 10
1608.2.br \(\chi_{1608}(277, \cdot)\) n/a 1360 10
1608.2.bs \(\chi_{1608}(143, \cdot)\) None 0 10
1608.2.bu \(\chi_{1608}(5, \cdot)\) n/a 2680 10
1608.2.bw \(\chi_{1608}(49, \cdot)\) n/a 680 20
1608.2.bx \(\chi_{1608}(35, \cdot)\) n/a 5360 20
1608.2.bz \(\chi_{1608}(41, \cdot)\) n/a 1360 20
1608.2.cc \(\chi_{1608}(115, \cdot)\) n/a 2720 20
1608.2.cf \(\chi_{1608}(101, \cdot)\) n/a 5360 20
1608.2.ch \(\chi_{1608}(23, \cdot)\) None 0 20
1608.2.ci \(\chi_{1608}(157, \cdot)\) n/a 2720 20
1608.2.ck \(\chi_{1608}(7, \cdot)\) None 0 20

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1608))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1608)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(201))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(268))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(402))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(536))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(804))\)\(^{\oplus 2}\)