Properties

Label 300.3
Level 300
Weight 3
Dimension 1895
Nonzero newspaces 12
Newform subspaces 39
Sturm bound 14400
Trace bound 7

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Defining parameters

Level: \( N \) = \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 39 \)
Sturm bound: \(14400\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(300))\).

Total New Old
Modular forms 5080 1975 3105
Cusp forms 4520 1895 2625
Eisenstein series 560 80 480

Trace form

\( 1895q - 2q^{2} + q^{3} - 24q^{4} - 12q^{5} - 28q^{6} - 54q^{7} - 8q^{8} - 57q^{9} + O(q^{10}) \) \( 1895q - 2q^{2} + q^{3} - 24q^{4} - 12q^{5} - 28q^{6} - 54q^{7} - 8q^{8} - 57q^{9} + 32q^{11} + 66q^{12} - 34q^{13} + 216q^{14} + 14q^{15} + 172q^{16} - 120q^{17} + 44q^{18} - 94q^{19} - 20q^{20} + 154q^{21} - 76q^{22} + 40q^{23} + 184q^{25} - 228q^{26} + 169q^{27} - 52q^{28} + 308q^{29} - 6q^{30} + 58q^{31} + 248q^{32} + 72q^{33} + 280q^{34} + 164q^{35} - 198q^{36} - 74q^{37} + 524q^{38} - 54q^{39} + 664q^{40} - 28q^{41} + 74q^{42} + 274q^{43} + 92q^{44} + 272q^{45} - 492q^{46} + 160q^{47} - 512q^{48} + 117q^{49} - 364q^{50} + 368q^{51} - 888q^{52} - 220q^{53} - 678q^{54} - 272q^{55} - 584q^{56} - 322q^{57} - 1388q^{58} - 800q^{59} - 1006q^{60} - 474q^{61} - 1260q^{62} - 176q^{63} - 552q^{64} - 120q^{65} + 678q^{66} - 414q^{67} + 488q^{68} - 14q^{69} + 468q^{70} + 160q^{71} + 1214q^{72} + 1110q^{73} + 828q^{74} + 98q^{75} + 1304q^{76} + 688q^{77} + 1160q^{78} + 1138q^{79} + 356q^{80} - 97q^{81} + 328q^{82} + 1120q^{83} - 298q^{84} + 1904q^{85} - 384q^{86} + 70q^{87} - 1780q^{88} + 784q^{89} - 970q^{90} - 540q^{91} - 2264q^{92} - 1208q^{93} - 2900q^{94} - 80q^{95} - 1918q^{96} - 1274q^{97} - 1594q^{98} - 1120q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(300))\)

We only show spaces with odd 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
300.3.b \(\chi_{300}(149, \cdot)\) 300.3.b.a 2 1
300.3.b.b 2
300.3.b.c 4
300.3.b.d 4
300.3.c \(\chi_{300}(151, \cdot)\) 300.3.c.a 2 1
300.3.c.b 2
300.3.c.c 2
300.3.c.d 8
300.3.c.e 8
300.3.c.f 8
300.3.c.g 8
300.3.f \(\chi_{300}(199, \cdot)\) 300.3.f.a 4 1
300.3.f.b 16
300.3.f.c 16
300.3.g \(\chi_{300}(101, \cdot)\) 300.3.g.a 1 1
300.3.g.b 1
300.3.g.c 1
300.3.g.d 2
300.3.g.e 2
300.3.g.f 2
300.3.g.g 2
300.3.g.h 2
300.3.k \(\chi_{300}(157, \cdot)\) 300.3.k.a 4 2
300.3.k.b 4
300.3.k.c 4
300.3.l \(\chi_{300}(107, \cdot)\) 300.3.l.a 4 2
300.3.l.b 4
300.3.l.c 4
300.3.l.d 4
300.3.l.e 8
300.3.l.f 8
300.3.l.g 40
300.3.l.h 64
300.3.p \(\chi_{300}(31, \cdot)\) 300.3.p.a 240 4
300.3.q \(\chi_{300}(29, \cdot)\) 300.3.q.a 80 4
300.3.s \(\chi_{300}(41, \cdot)\) 300.3.s.a 80 4
300.3.t \(\chi_{300}(19, \cdot)\) 300.3.t.a 240 4
300.3.u \(\chi_{300}(23, \cdot)\) 300.3.u.a 928 8
300.3.v \(\chi_{300}(13, \cdot)\) 300.3.v.a 80 8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(300))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(300)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)