Properties

Label 675.2
Level 675
Weight 2
Dimension 11469
Nonzero newspaces 18
Newforms 76
Sturm bound 64800
Trace bound 4

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Defining parameters

Level: \( N \) = \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Newforms: \( 76 \)
Sturm bound: \(64800\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(675))\).

Total New Old
Modular forms 17040 12125 4915
Cusp forms 15361 11469 3892
Eisenstein series 1679 656 1023

Trace form

\(11469q \) \(\mathstrut -\mathstrut 54q^{2} \) \(\mathstrut -\mathstrut 78q^{3} \) \(\mathstrut -\mathstrut 92q^{4} \) \(\mathstrut -\mathstrut 64q^{5} \) \(\mathstrut -\mathstrut 120q^{6} \) \(\mathstrut -\mathstrut 91q^{7} \) \(\mathstrut -\mathstrut 26q^{8} \) \(\mathstrut -\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(11469q \) \(\mathstrut -\mathstrut 54q^{2} \) \(\mathstrut -\mathstrut 78q^{3} \) \(\mathstrut -\mathstrut 92q^{4} \) \(\mathstrut -\mathstrut 64q^{5} \) \(\mathstrut -\mathstrut 120q^{6} \) \(\mathstrut -\mathstrut 91q^{7} \) \(\mathstrut -\mathstrut 26q^{8} \) \(\mathstrut -\mathstrut 72q^{9} \) \(\mathstrut -\mathstrut 104q^{10} \) \(\mathstrut -\mathstrut 61q^{11} \) \(\mathstrut -\mathstrut 60q^{12} \) \(\mathstrut -\mathstrut 69q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 96q^{15} \) \(\mathstrut -\mathstrut 104q^{16} \) \(\mathstrut -\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 63q^{18} \) \(\mathstrut -\mathstrut 78q^{19} \) \(\mathstrut -\mathstrut 32q^{20} \) \(\mathstrut -\mathstrut 132q^{21} \) \(\mathstrut -\mathstrut 33q^{22} \) \(\mathstrut -\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 90q^{24} \) \(\mathstrut -\mathstrut 96q^{25} \) \(\mathstrut -\mathstrut 126q^{26} \) \(\mathstrut -\mathstrut 81q^{27} \) \(\mathstrut -\mathstrut 170q^{28} \) \(\mathstrut +\mathstrut 2q^{29} \) \(\mathstrut -\mathstrut 96q^{30} \) \(\mathstrut -\mathstrut 109q^{31} \) \(\mathstrut -\mathstrut 112q^{32} \) \(\mathstrut -\mathstrut 96q^{33} \) \(\mathstrut -\mathstrut 75q^{34} \) \(\mathstrut -\mathstrut 100q^{35} \) \(\mathstrut -\mathstrut 246q^{36} \) \(\mathstrut -\mathstrut 92q^{37} \) \(\mathstrut -\mathstrut 174q^{38} \) \(\mathstrut -\mathstrut 159q^{39} \) \(\mathstrut -\mathstrut 192q^{40} \) \(\mathstrut -\mathstrut 209q^{41} \) \(\mathstrut -\mathstrut 246q^{42} \) \(\mathstrut -\mathstrut 201q^{43} \) \(\mathstrut -\mathstrut 421q^{44} \) \(\mathstrut -\mathstrut 156q^{45} \) \(\mathstrut -\mathstrut 223q^{46} \) \(\mathstrut -\mathstrut 231q^{47} \) \(\mathstrut -\mathstrut 327q^{48} \) \(\mathstrut -\mathstrut 158q^{49} \) \(\mathstrut -\mathstrut 184q^{50} \) \(\mathstrut -\mathstrut 354q^{51} \) \(\mathstrut -\mathstrut 197q^{52} \) \(\mathstrut -\mathstrut 186q^{53} \) \(\mathstrut -\mathstrut 270q^{54} \) \(\mathstrut -\mathstrut 248q^{55} \) \(\mathstrut -\mathstrut 241q^{56} \) \(\mathstrut -\mathstrut 147q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 8q^{59} \) \(\mathstrut -\mathstrut 168q^{60} \) \(\mathstrut -\mathstrut 73q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 63q^{63} \) \(\mathstrut -\mathstrut 144q^{64} \) \(\mathstrut -\mathstrut 96q^{65} \) \(\mathstrut -\mathstrut 129q^{66} \) \(\mathstrut -\mathstrut 78q^{67} \) \(\mathstrut -\mathstrut 223q^{68} \) \(\mathstrut -\mathstrut 63q^{69} \) \(\mathstrut -\mathstrut 240q^{70} \) \(\mathstrut +\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 246q^{72} \) \(\mathstrut -\mathstrut 149q^{73} \) \(\mathstrut -\mathstrut 371q^{74} \) \(\mathstrut -\mathstrut 168q^{75} \) \(\mathstrut -\mathstrut 506q^{76} \) \(\mathstrut -\mathstrut 393q^{77} \) \(\mathstrut -\mathstrut 366q^{78} \) \(\mathstrut -\mathstrut 333q^{79} \) \(\mathstrut -\mathstrut 552q^{80} \) \(\mathstrut -\mathstrut 276q^{81} \) \(\mathstrut -\mathstrut 684q^{82} \) \(\mathstrut -\mathstrut 493q^{83} \) \(\mathstrut -\mathstrut 522q^{84} \) \(\mathstrut -\mathstrut 256q^{85} \) \(\mathstrut -\mathstrut 757q^{86} \) \(\mathstrut -\mathstrut 303q^{87} \) \(\mathstrut -\mathstrut 546q^{88} \) \(\mathstrut -\mathstrut 579q^{89} \) \(\mathstrut -\mathstrut 324q^{90} \) \(\mathstrut -\mathstrut 371q^{91} \) \(\mathstrut -\mathstrut 847q^{92} \) \(\mathstrut -\mathstrut 399q^{93} \) \(\mathstrut -\mathstrut 387q^{94} \) \(\mathstrut -\mathstrut 212q^{95} \) \(\mathstrut -\mathstrut 552q^{96} \) \(\mathstrut -\mathstrut 212q^{97} \) \(\mathstrut -\mathstrut 725q^{98} \) \(\mathstrut -\mathstrut 339q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(675))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
675.2.a \(\chi_{675}(1, \cdot)\) 675.2.a.a 1 1
675.2.a.b 1
675.2.a.c 1
675.2.a.d 1
675.2.a.e 1
675.2.a.f 1
675.2.a.g 1
675.2.a.h 1
675.2.a.i 1
675.2.a.j 2
675.2.a.k 2
675.2.a.l 2
675.2.a.m 2
675.2.a.n 2
675.2.a.o 2
675.2.a.p 2
675.2.a.q 2
675.2.b \(\chi_{675}(649, \cdot)\) 675.2.b.a 2 1
675.2.b.b 2
675.2.b.c 2
675.2.b.d 2
675.2.b.e 2
675.2.b.f 2
675.2.b.g 4
675.2.b.h 4
675.2.b.i 4
675.2.e \(\chi_{675}(226, \cdot)\) 675.2.e.a 2 2
675.2.e.b 6
675.2.e.c 8
675.2.e.d 8
675.2.e.e 8
675.2.f \(\chi_{675}(107, \cdot)\) 675.2.f.a 4 2
675.2.f.b 4
675.2.f.c 4
675.2.f.d 4
675.2.f.e 4
675.2.f.f 4
675.2.f.g 8
675.2.f.h 8
675.2.f.i 8
675.2.h \(\chi_{675}(136, \cdot)\) 675.2.h.a 40 4
675.2.h.b 40
675.2.h.c 40
675.2.h.d 40
675.2.k \(\chi_{675}(199, \cdot)\) 675.2.k.a 4 2
675.2.k.b 12
675.2.k.c 16
675.2.l \(\chi_{675}(76, \cdot)\) 675.2.l.a 6 6
675.2.l.b 6
675.2.l.c 12
675.2.l.d 30
675.2.l.e 42
675.2.l.f 66
675.2.l.g 66
675.2.l.h 96
675.2.n \(\chi_{675}(109, \cdot)\) 675.2.n.a 80 4
675.2.n.b 80
675.2.q \(\chi_{675}(143, \cdot)\) 675.2.q.a 16 4
675.2.q.b 16
675.2.q.c 32
675.2.r \(\chi_{675}(46, \cdot)\) 675.2.r.a 224 8
675.2.u \(\chi_{675}(49, \cdot)\) 675.2.u.a 12 6
675.2.u.b 24
675.2.u.c 60
675.2.u.d 84
675.2.u.e 132
675.2.w \(\chi_{675}(53, \cdot)\) 675.2.w.a 160 8
675.2.w.b 160
675.2.y \(\chi_{675}(19, \cdot)\) 675.2.y.a 224 8
675.2.ba \(\chi_{675}(32, \cdot)\) 675.2.ba.a 144 12
675.2.ba.b 192
675.2.ba.c 288
675.2.bc \(\chi_{675}(16, \cdot)\) 675.2.bc.a 2112 24
675.2.bd \(\chi_{675}(8, \cdot)\) 675.2.bd.a 448 16
675.2.bg \(\chi_{675}(4, \cdot)\) 675.2.bg.a 2112 24
675.2.bi \(\chi_{675}(2, \cdot)\) 675.2.bi.a 4224 48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(675))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(675)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)