↑

Properties

Label 679.2
Level 679
Weight 2
Dimension 17551
Nonzero newspaces 30
Newform subspaces 42
Sturm bound 75264
Trace bound 26

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 679 = 7 \cdot 97 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Newform subspaces: \( 42 \)
Sturm bound: \(75264\)
Trace bound: \(26\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(679))\).

Total New Old
Modular forms 19392 18503 889
Cusp forms 18241 17551 690
Eisenstein series 1151 952 199

Trace form

\( 17551 q - 195 q^{2} - 196 q^{3} - 199 q^{4} - 198 q^{5} - 204 q^{6} - 241 q^{7} - 495 q^{8} - 205 q^{9} + O(q^{10}) \) \( 17551 q - 195 q^{2} - 196 q^{3} - 199 q^{4} - 198 q^{5} - 204 q^{6} - 241 q^{7} - 495 q^{8} - 205 q^{9} - 210 q^{10} - 204 q^{11} - 220 q^{12} - 206 q^{13} - 243 q^{14} - 504 q^{15} - 223 q^{16} - 210 q^{17} - 231 q^{18} - 212 q^{19} - 234 q^{20} - 244 q^{21} - 516 q^{22} - 216 q^{23} - 252 q^{24} - 223 q^{25} - 234 q^{26} - 232 q^{27} - 247 q^{28} - 510 q^{29} - 264 q^{30} - 224 q^{31} - 255 q^{32} - 240 q^{33} - 246 q^{34} - 246 q^{35} - 571 q^{36} - 230 q^{37} - 252 q^{38} - 248 q^{39} - 282 q^{40} - 234 q^{41} - 252 q^{42} - 524 q^{43} - 276 q^{44} - 270 q^{45} - 264 q^{46} - 240 q^{47} - 316 q^{48} - 241 q^{49} - 573 q^{50} - 264 q^{51} - 290 q^{52} - 246 q^{53} - 312 q^{54} - 264 q^{55} - 255 q^{56} - 560 q^{57} - 282 q^{58} - 252 q^{59} - 360 q^{60} - 254 q^{61} - 288 q^{62} - 253 q^{63} - 607 q^{64} - 276 q^{65} - 336 q^{66} - 260 q^{67} - 318 q^{68} - 288 q^{69} - 258 q^{70} - 552 q^{71} - 387 q^{72} - 266 q^{73} - 306 q^{74} - 316 q^{75} - 332 q^{76} - 252 q^{77} - 648 q^{78} - 144 q^{79} - 42 q^{80} - 25 q^{81} + 66 q^{82} - 180 q^{83} + 84 q^{84} - 204 q^{85} + 252 q^{86} - 120 q^{87} + 492 q^{88} + 6 q^{89} + 390 q^{90} + 34 q^{91} - 72 q^{92} + 96 q^{93} + 48 q^{94} - 24 q^{95} + 996 q^{96} + 191 q^{97} - 291 q^{98} - 156 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(679))\)

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
679.2.a \(\chi_{679}(1, \cdot)\) 679.2.a.a 2 1
679.2.a.b 4
679.2.a.c 4
679.2.a.d 8
679.2.a.e 14
679.2.a.f 17
679.2.d \(\chi_{679}(484, \cdot)\) 679.2.d.a 50 1
679.2.e \(\chi_{679}(449, \cdot)\) 679.2.e.a 2 2
679.2.e.b 48
679.2.e.c 50
679.2.f \(\chi_{679}(389, \cdot)\) 679.2.f.a 2 2
679.2.f.b 4
679.2.f.c 54
679.2.f.d 68
679.2.g \(\chi_{679}(326, \cdot)\) 679.2.g.a 2 2
679.2.g.b 124
679.2.h \(\chi_{679}(158, \cdot)\) 679.2.h.a 2 2
679.2.h.b 124
679.2.i \(\chi_{679}(22, \cdot)\) 679.2.i.a 100 2
679.2.m \(\chi_{679}(36, \cdot)\) 679.2.m.a 100 2
679.2.n \(\chi_{679}(193, \cdot)\) 679.2.n.a 128 2
679.2.s \(\chi_{679}(256, \cdot)\) 679.2.s.a 126 2
679.2.t \(\chi_{679}(424, \cdot)\) 679.2.t.a 126 2
679.2.x \(\chi_{679}(50, \cdot)\) 679.2.x.a 200 4
679.2.z \(\chi_{679}(81, \cdot)\) 679.2.z.a 252 4
679.2.ba \(\chi_{679}(16, \cdot)\) 679.2.ba.a 252 4
679.2.bd \(\chi_{679}(113, \cdot)\) 679.2.bd.a 200 4
679.2.be \(\chi_{679}(172, \cdot)\) 679.2.be.a 256 4
679.2.bg \(\chi_{679}(8, \cdot)\) 679.2.bg.a 384 8
679.2.bi \(\chi_{679}(9, \cdot)\) 679.2.bi.a 504 8
679.2.bl \(\chi_{679}(4, \cdot)\) 679.2.bl.a 504 8
679.2.bm \(\chi_{679}(43, \cdot)\) 679.2.bm.a 400 8
679.2.bp \(\chi_{679}(130, \cdot)\) 679.2.bp.a 512 8
679.2.bq \(\chi_{679}(20, \cdot)\) 679.2.bq.a 992 16
679.2.bs \(\chi_{679}(18, \cdot)\) 679.2.bs.a 1024 16
679.2.bw \(\chi_{679}(53, \cdot)\) 679.2.bw.a 1008 16
679.2.bx \(\chi_{679}(99, \cdot)\) 679.2.bx.a 768 16
679.2.by \(\chi_{679}(2, \cdot)\) 679.2.by.a 1008 16
679.2.cb \(\chi_{679}(19, \cdot)\) 679.2.cb.a 2048 32
679.2.cc \(\chi_{679}(26, \cdot)\) 679.2.cc.a 2016 32
679.2.cf \(\chi_{679}(5, \cdot)\) 679.2.cf.a 2016 32
679.2.cg \(\chi_{679}(13, \cdot)\) 679.2.cg.a 2048 32

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(679))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(679)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(97))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(679))\)\(^{\oplus 1}\)