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Properties

Label 1050.3
Level 1050
Weight 3
Dimension 12720
Nonzero newspaces 24
Sturm bound 172800
Trace bound 7

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Defining parameters

Level: \( N \) = \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(172800\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1050))\).

Total New Old
Modular forms 58944 12720 46224
Cusp forms 56256 12720 43536
Eisenstein series 2688 0 2688

Trace form

\( 12720 q + 16 q^{2} + 22 q^{3} + 8 q^{4} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 142 q^{9} + O(q^{10}) \) \( 12720 q + 16 q^{2} + 22 q^{3} + 8 q^{4} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 142 q^{9} - 24 q^{10} - 100 q^{11} - 44 q^{12} - 140 q^{13} + 8 q^{15} + 64 q^{16} - 432 q^{17} + 32 q^{18} - 520 q^{19} - 64 q^{20} - 10 q^{21} - 192 q^{22} - 176 q^{23} + 24 q^{24} - 120 q^{25} - 416 q^{26} - 644 q^{27} - 312 q^{28} - 40 q^{29} + 192 q^{30} - 152 q^{31} + 96 q^{32} + 282 q^{33} + 360 q^{34} + 472 q^{35} + 24 q^{36} - 132 q^{37} + 536 q^{38} + 156 q^{39} - 48 q^{40} + 832 q^{41} + 920 q^{42} + 1248 q^{43} + 888 q^{44} + 32 q^{45} + 1400 q^{46} + 1180 q^{47} + 64 q^{48} + 348 q^{49} + 184 q^{50} + 758 q^{51} + 280 q^{52} + 1024 q^{53} + 816 q^{54} + 1216 q^{55} + 32 q^{56} + 676 q^{57} - 128 q^{58} - 344 q^{59} + 416 q^{60} - 2256 q^{61} - 320 q^{62} + 1046 q^{63} - 64 q^{64} - 664 q^{65} + 16 q^{66} - 1592 q^{67} - 256 q^{68} + 852 q^{69} - 48 q^{70} + 832 q^{71} - 112 q^{72} + 1964 q^{73} + 240 q^{74} - 232 q^{75} + 8 q^{76} + 2192 q^{77} + 32 q^{78} + 2384 q^{79} - 442 q^{81} + 1136 q^{82} + 2176 q^{83} - 132 q^{84} + 48 q^{85} + 120 q^{86} + 196 q^{87} - 400 q^{88} - 272 q^{89} - 504 q^{90} - 672 q^{91} - 176 q^{92} + 1654 q^{93} - 1736 q^{94} - 512 q^{95} + 208 q^{96} + 1104 q^{97} - 48 q^{98} + 2324 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1050))\)

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
1050.3.c \(\chi_{1050}(449, \cdot)\) 1050.3.c.a 8 1
1050.3.c.b 32
1050.3.c.c 32
1050.3.e \(\chi_{1050}(701, \cdot)\) 1050.3.e.a 4 1
1050.3.e.b 16
1050.3.e.c 16
1050.3.e.d 16
1050.3.e.e 24
1050.3.f \(\chi_{1050}(601, \cdot)\) 1050.3.f.a 4 1
1050.3.f.b 8
1050.3.f.c 12
1050.3.f.d 12
1050.3.f.e 16
1050.3.h \(\chi_{1050}(349, \cdot)\) 1050.3.h.a 8 1
1050.3.h.b 16
1050.3.h.c 24
1050.3.k \(\chi_{1050}(293, \cdot)\) n/a 192 2
1050.3.l \(\chi_{1050}(43, \cdot)\) 1050.3.l.a 8 2
1050.3.l.b 8
1050.3.l.c 8
1050.3.l.d 8
1050.3.l.e 8
1050.3.l.f 8
1050.3.l.g 8
1050.3.l.h 16
1050.3.p \(\chi_{1050}(451, \cdot)\) 1050.3.p.a 4 2
1050.3.p.b 8
1050.3.p.c 8
1050.3.p.d 8
1050.3.p.e 12
1050.3.p.f 12
1050.3.p.g 16
1050.3.p.h 16
1050.3.p.i 16
1050.3.q \(\chi_{1050}(199, \cdot)\) 1050.3.q.a 8 2
1050.3.q.b 16
1050.3.q.c 16
1050.3.q.d 24
1050.3.q.e 32
1050.3.r \(\chi_{1050}(149, \cdot)\) n/a 192 2
1050.3.t \(\chi_{1050}(401, \cdot)\) n/a 204 2
1050.3.v \(\chi_{1050}(139, \cdot)\) n/a 320 4
1050.3.x \(\chi_{1050}(181, \cdot)\) n/a 320 4
1050.3.y \(\chi_{1050}(71, \cdot)\) n/a 480 4
1050.3.ba \(\chi_{1050}(29, \cdot)\) n/a 480 4
1050.3.bd \(\chi_{1050}(193, \cdot)\) n/a 192 4
1050.3.be \(\chi_{1050}(143, \cdot)\) n/a 384 4
1050.3.bi \(\chi_{1050}(127, \cdot)\) n/a 480 8
1050.3.bj \(\chi_{1050}(83, \cdot)\) n/a 1280 8
1050.3.bm \(\chi_{1050}(11, \cdot)\) n/a 1280 8
1050.3.bo \(\chi_{1050}(179, \cdot)\) n/a 1280 8
1050.3.bp \(\chi_{1050}(19, \cdot)\) n/a 640 8
1050.3.bq \(\chi_{1050}(31, \cdot)\) n/a 640 8
1050.3.bt \(\chi_{1050}(17, \cdot)\) n/a 2560 16
1050.3.bu \(\chi_{1050}(37, \cdot)\) n/a 1280 16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1050))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1050)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 2}\)