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Properties

Label 676.2
Level 676
Weight 2
Dimension 7979
Nonzero newspaces 12
Newform subspaces 57
Sturm bound 56784
Trace bound 1

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Defining parameters

Level: \( N \) = \( 676 = 2^{2} \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 57 \)
Sturm bound: \(56784\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(676))\).

Total New Old
Modular forms 14766 8387 6379
Cusp forms 13627 7979 5648
Eisenstein series 1139 408 731

Trace form

\( 7979 q - 66 q^{2} - 66 q^{4} - 132 q^{5} - 66 q^{6} + 4 q^{7} - 66 q^{8} - 116 q^{9} + O(q^{10}) \) \( 7979 q - 66 q^{2} - 66 q^{4} - 132 q^{5} - 66 q^{6} + 4 q^{7} - 66 q^{8} - 116 q^{9} - 66 q^{10} + 12 q^{11} - 78 q^{12} - 132 q^{13} - 126 q^{14} + 24 q^{15} - 66 q^{16} - 126 q^{17} - 102 q^{18} - 8 q^{19} - 114 q^{20} - 176 q^{21} - 126 q^{22} - 24 q^{23} - 162 q^{24} - 186 q^{25} - 102 q^{26} - 72 q^{27} - 126 q^{28} - 138 q^{29} - 162 q^{30} + 4 q^{31} - 126 q^{32} - 144 q^{33} - 114 q^{34} + 36 q^{35} - 66 q^{36} - 110 q^{37} - 78 q^{38} + 20 q^{39} - 78 q^{40} - 150 q^{41} - 30 q^{42} - 4 q^{43} - 6 q^{44} - 162 q^{45} + 54 q^{46} + 12 q^{47} + 30 q^{48} - 256 q^{49} + 18 q^{50} - 18 q^{52} - 300 q^{53} + 18 q^{54} - 12 q^{55} + 42 q^{56} - 224 q^{57} + 30 q^{58} + 12 q^{59} - 6 q^{60} - 198 q^{61} - 42 q^{62} + 4 q^{63} - 78 q^{64} - 189 q^{65} - 198 q^{66} - 8 q^{67} - 222 q^{68} - 120 q^{69} - 150 q^{70} - 72 q^{71} - 222 q^{72} - 188 q^{73} - 234 q^{74} - 32 q^{75} - 186 q^{76} - 180 q^{77} - 186 q^{78} + 24 q^{79} - 294 q^{80} - 224 q^{81} - 186 q^{82} - 84 q^{83} - 150 q^{84} - 150 q^{85} - 174 q^{86} - 24 q^{87} - 150 q^{88} - 132 q^{89} - 78 q^{90} + 2 q^{91} - 174 q^{92} - 104 q^{93} - 42 q^{94} + 114 q^{96} - 20 q^{97} - 42 q^{98} + 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(676))\)

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
676.2.a \(\chi_{676}(1, \cdot)\) 676.2.a.a 1 1
676.2.a.b 1
676.2.a.c 1
676.2.a.d 1
676.2.a.e 1
676.2.a.f 2
676.2.a.g 3
676.2.a.h 3
676.2.d \(\chi_{676}(337, \cdot)\) 676.2.d.a 2 1
676.2.d.b 2
676.2.d.c 2
676.2.d.d 2
676.2.d.e 6
676.2.e \(\chi_{676}(529, \cdot)\) 676.2.e.a 2 2
676.2.e.b 2
676.2.e.c 2
676.2.e.d 2
676.2.e.e 4
676.2.e.f 6
676.2.e.g 6
676.2.f \(\chi_{676}(99, \cdot)\) 676.2.f.a 2 2
676.2.f.b 2
676.2.f.c 2
676.2.f.d 4
676.2.f.e 4
676.2.f.f 8
676.2.f.g 8
676.2.f.h 16
676.2.f.i 16
676.2.f.j 72
676.2.h \(\chi_{676}(361, \cdot)\) 676.2.h.a 2 2
676.2.h.b 4
676.2.h.c 4
676.2.h.d 4
676.2.h.e 12
676.2.l \(\chi_{676}(19, \cdot)\) 676.2.l.a 4 4
676.2.l.b 4
676.2.l.c 4
676.2.l.d 4
676.2.l.e 4
676.2.l.f 4
676.2.l.g 4
676.2.l.h 16
676.2.l.i 16
676.2.l.j 16
676.2.l.k 16
676.2.l.l 16
676.2.l.m 16
676.2.l.n 144
676.2.m \(\chi_{676}(53, \cdot)\) 676.2.m.a 180 12
676.2.n \(\chi_{676}(25, \cdot)\) 676.2.n.a 168 12
676.2.q \(\chi_{676}(9, \cdot)\) 676.2.q.a 384 24
676.2.s \(\chi_{676}(31, \cdot)\) 676.2.s.a 24 24
676.2.s.b 2112
676.2.v \(\chi_{676}(17, \cdot)\) 676.2.v.a 360 24
676.2.w \(\chi_{676}(7, \cdot)\) 676.2.w.a 48 48
676.2.w.b 4224

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(676))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(676)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)