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Properties

Label 696.2
Level 696
Weight 2
Dimension 5548
Nonzero newspaces 18
Newform subspaces 51
Sturm bound 53760
Trace bound 4

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Defining parameters

Level: \( N \) = \( 696 = 2^{3} \cdot 3 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Newform subspaces: \( 51 \)
Sturm bound: \(53760\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(696))\).

Total New Old
Modular forms 14112 5764 8348
Cusp forms 12769 5548 7221
Eisenstein series 1343 216 1127

Trace form

\( 5548 q + 4 q^{2} - 22 q^{3} - 48 q^{4} + 4 q^{5} - 32 q^{6} - 48 q^{7} - 8 q^{8} - 50 q^{9} + O(q^{10}) \) \( 5548 q + 4 q^{2} - 22 q^{3} - 48 q^{4} + 4 q^{5} - 32 q^{6} - 48 q^{7} - 8 q^{8} - 50 q^{9} - 64 q^{10} - 8 q^{11} - 44 q^{12} + 4 q^{13} - 8 q^{14} - 40 q^{15} - 56 q^{16} + 4 q^{17} - 16 q^{18} - 56 q^{19} + 16 q^{20} - 40 q^{22} - 4 q^{24} - 94 q^{25} + 16 q^{26} - 46 q^{27} - 56 q^{28} - 6 q^{29} - 48 q^{30} - 80 q^{31} - 16 q^{32} - 64 q^{33} - 96 q^{34} - 36 q^{36} - 12 q^{37} - 16 q^{38} - 16 q^{39} - 72 q^{40} + 4 q^{41} - 36 q^{42} - 24 q^{43} + 18 q^{45} - 40 q^{46} + 104 q^{47} - 12 q^{48} - 2 q^{49} + 4 q^{50} + 64 q^{51} - 88 q^{52} + 130 q^{53} - 40 q^{54} + 184 q^{55} + 16 q^{56} - 16 q^{57} - 44 q^{58} + 48 q^{59} - 28 q^{60} + 116 q^{61} + 8 q^{62} - 8 q^{63} - 24 q^{64} + 86 q^{65} - 44 q^{66} + 8 q^{67} + 40 q^{69} - 40 q^{70} - 8 q^{71} - 52 q^{72} - 46 q^{73} - 32 q^{74} - 50 q^{75} - 8 q^{76} - 44 q^{78} - 80 q^{79} - 34 q^{81} + 16 q^{82} + 8 q^{83} - 96 q^{84} + 8 q^{85} + 16 q^{86} - 10 q^{87} - 144 q^{88} + 52 q^{89} - 20 q^{90} - 56 q^{91} + 16 q^{93} - 104 q^{94} + 16 q^{95} - 160 q^{96} - 110 q^{97} - 292 q^{98} - 172 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(696))\)

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
696.2.a \(\chi_{696}(1, \cdot)\) 696.2.a.a 1 1
696.2.a.b 1
696.2.a.c 1
696.2.a.d 1
696.2.a.e 1
696.2.a.f 1
696.2.a.g 1
696.2.a.h 2
696.2.a.i 2
696.2.a.j 3
696.2.c \(\chi_{696}(695, \cdot)\) None 0 1
696.2.e \(\chi_{696}(407, \cdot)\) None 0 1
696.2.f \(\chi_{696}(349, \cdot)\) 696.2.f.a 4 1
696.2.f.b 18
696.2.f.c 34
696.2.h \(\chi_{696}(637, \cdot)\) 696.2.h.a 30 1
696.2.h.b 30
696.2.j \(\chi_{696}(59, \cdot)\) 696.2.j.a 56 1
696.2.j.b 56
696.2.l \(\chi_{696}(347, \cdot)\) 696.2.l.a 12 1
696.2.l.b 104
696.2.o \(\chi_{696}(289, \cdot)\) 696.2.o.a 2 1
696.2.o.b 2
696.2.o.c 4
696.2.o.d 6
696.2.q \(\chi_{696}(655, \cdot)\) None 0 2
696.2.t \(\chi_{696}(365, \cdot)\) 696.2.t.a 4 2
696.2.t.b 4
696.2.t.c 4
696.2.t.d 4
696.2.t.e 4
696.2.t.f 4
696.2.t.g 208
696.2.v \(\chi_{696}(307, \cdot)\) 696.2.v.a 4 2
696.2.v.b 4
696.2.v.c 112
696.2.w \(\chi_{696}(17, \cdot)\) 696.2.w.a 60 2
696.2.y \(\chi_{696}(25, \cdot)\) 696.2.y.a 6 6
696.2.y.b 18
696.2.y.c 24
696.2.y.d 24
696.2.y.e 24
696.2.ba \(\chi_{696}(121, \cdot)\) 696.2.ba.a 36 6
696.2.ba.b 48
696.2.bd \(\chi_{696}(35, \cdot)\) 696.2.bd.a 696 6
696.2.bf \(\chi_{696}(83, \cdot)\) 696.2.bf.a 696 6
696.2.bh \(\chi_{696}(13, \cdot)\) 696.2.bh.a 180 6
696.2.bh.b 180
696.2.bj \(\chi_{696}(181, \cdot)\) 696.2.bj.a 360 6
696.2.bk \(\chi_{696}(23, \cdot)\) None 0 6
696.2.bm \(\chi_{696}(71, \cdot)\) None 0 6
696.2.bp \(\chi_{696}(89, \cdot)\) 696.2.bp.a 360 12
696.2.bq \(\chi_{696}(19, \cdot)\) 696.2.bq.a 720 12
696.2.bs \(\chi_{696}(77, \cdot)\) 696.2.bs.a 24 12
696.2.bs.b 24
696.2.bs.c 1344
696.2.bv \(\chi_{696}(31, \cdot)\) None 0 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(696))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(696)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(348))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(696))\)\(^{\oplus 1}\)