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Properties

Label 105.3
Level 105
Weight 3
Dimension 476
Nonzero newspaces 12
Newform subspaces 18
Sturm bound 2304
Trace bound 4

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Defining parameters

Level: \( N \) = \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 18 \)
Sturm bound: \(2304\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(105))\).

Total New Old
Modular forms 864 540 324
Cusp forms 672 476 196
Eisenstein series 192 64 128

Trace form

\( 476 q + 8 q^{2} + 8 q^{3} + 36 q^{4} + 14 q^{5} + 4 q^{6} - 20 q^{7} - 12 q^{8} + 4 q^{9} + O(q^{10}) \) \( 476 q + 8 q^{2} + 8 q^{3} + 36 q^{4} + 14 q^{5} + 4 q^{6} - 20 q^{7} - 12 q^{8} + 4 q^{9} - 60 q^{10} - 44 q^{11} - 104 q^{12} - 28 q^{13} - 48 q^{14} - 40 q^{15} - 132 q^{16} - 16 q^{17} - 100 q^{18} + 68 q^{19} + 72 q^{20} + 24 q^{21} + 88 q^{22} + 80 q^{23} - 48 q^{24} - 220 q^{25} - 308 q^{26} - 88 q^{27} - 452 q^{28} - 216 q^{29} - 236 q^{30} - 268 q^{31} - 292 q^{32} - 332 q^{33} - 512 q^{34} - 98 q^{35} - 172 q^{36} - 192 q^{37} + 228 q^{38} + 284 q^{39} + 728 q^{40} + 448 q^{41} + 756 q^{42} + 712 q^{43} + 1296 q^{44} + 430 q^{45} + 952 q^{46} + 500 q^{47} + 592 q^{48} + 144 q^{49} - 364 q^{50} + 40 q^{51} - 488 q^{52} - 88 q^{53} + 124 q^{54} - 564 q^{55} - 1284 q^{56} - 688 q^{57} - 1832 q^{58} - 1128 q^{59} - 1220 q^{60} - 1532 q^{61} - 1688 q^{62} - 336 q^{63} - 1308 q^{64} - 370 q^{65} - 352 q^{66} - 308 q^{67} - 128 q^{68} - 72 q^{69} + 516 q^{70} + 496 q^{71} + 216 q^{72} + 1088 q^{73} + 1140 q^{74} + 296 q^{75} + 1656 q^{76} + 920 q^{77} + 664 q^{78} + 628 q^{79} + 2000 q^{80} + 40 q^{81} + 2064 q^{82} + 1376 q^{83} + 1680 q^{84} + 1512 q^{85} + 1660 q^{86} + 896 q^{87} + 1416 q^{88} + 120 q^{89} + 1496 q^{90} + 456 q^{91} - 40 q^{92} + 1440 q^{93} + 1120 q^{94} + 150 q^{95} + 2828 q^{96} + 1432 q^{97} + 924 q^{98} + 1160 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
105.3.c \(\chi_{105}(71, \cdot)\) 105.3.c.a 16 1
105.3.e \(\chi_{105}(34, \cdot)\) 105.3.e.a 16 1
105.3.f \(\chi_{105}(29, \cdot)\) 105.3.f.a 24 1
105.3.h \(\chi_{105}(76, \cdot)\) 105.3.h.a 12 1
105.3.k \(\chi_{105}(62, \cdot)\) 105.3.k.a 4 2
105.3.k.b 4
105.3.k.c 16
105.3.k.d 32
105.3.l \(\chi_{105}(22, \cdot)\) 105.3.l.a 24 2
105.3.n \(\chi_{105}(31, \cdot)\) 105.3.n.a 8 2
105.3.n.b 12
105.3.o \(\chi_{105}(44, \cdot)\) 105.3.o.a 16 2
105.3.o.b 40
105.3.r \(\chi_{105}(19, \cdot)\) 105.3.r.a 32 2
105.3.t \(\chi_{105}(11, \cdot)\) 105.3.t.a 8 2
105.3.t.b 36
105.3.v \(\chi_{105}(37, \cdot)\) 105.3.v.a 64 4
105.3.w \(\chi_{105}(17, \cdot)\) 105.3.w.a 112 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(105))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(105)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)