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Properties

Label 1470.3
Level 1470
Weight 3
Dimension 24828
Nonzero newspaces 24
Sturm bound 338688
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(338688\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1470))\).

Total New Old
Modular forms 114816 24828 89988
Cusp forms 110976 24828 86148
Eisenstein series 3840 0 3840

Trace form

\( 24828 q + 4 q^{2} + 28 q^{3} + 32 q^{4} + 24 q^{5} - 8 q^{6} - 32 q^{7} - 8 q^{8} + 32 q^{9} + O(q^{10}) \) \( 24828 q + 4 q^{2} + 28 q^{3} + 32 q^{4} + 24 q^{5} - 8 q^{6} - 32 q^{7} - 8 q^{8} + 32 q^{9} - 108 q^{10} - 160 q^{11} - 56 q^{12} - 140 q^{13} - 164 q^{15} + 16 q^{16} - 148 q^{17} - 52 q^{18} - 80 q^{19} + 8 q^{20} - 36 q^{21} + 32 q^{22} + 176 q^{23} + 96 q^{24} - 564 q^{25} - 360 q^{26} + 28 q^{27} - 144 q^{28} - 480 q^{29} - 312 q^{30} - 720 q^{31} - 16 q^{32} - 672 q^{33} - 160 q^{34} + 12 q^{35} - 120 q^{36} - 1684 q^{37} - 880 q^{38} - 940 q^{39} - 504 q^{40} - 976 q^{41} - 576 q^{42} + 408 q^{43} + 1260 q^{45} - 64 q^{46} + 480 q^{47} + 16 q^{48} + 408 q^{49} + 236 q^{50} + 800 q^{51} - 216 q^{52} + 1396 q^{53} - 336 q^{54} + 1052 q^{55} + 1152 q^{56} - 448 q^{57} + 1888 q^{58} + 1680 q^{59} + 216 q^{60} + 2504 q^{61} + 2272 q^{62} + 840 q^{63} - 256 q^{64} - 516 q^{65} + 1024 q^{66} + 1096 q^{67} + 296 q^{68} + 808 q^{69} + 504 q^{70} + 1216 q^{71} + 152 q^{72} + 3068 q^{73} + 960 q^{74} + 1328 q^{75} + 1472 q^{76} + 1440 q^{77} + 1288 q^{78} + 4016 q^{79} - 96 q^{80} - 2676 q^{81} + 1184 q^{82} - 1824 q^{83} - 24 q^{84} + 1252 q^{85} - 960 q^{86} - 1152 q^{87} - 640 q^{88} - 2976 q^{89} + 1380 q^{90} - 2912 q^{91} - 224 q^{92} - 568 q^{93} - 2144 q^{94} - 1352 q^{95} + 160 q^{96} - 1364 q^{97} - 384 q^{98} + 3008 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1470))\)

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
1470.3.c \(\chi_{1470}(1079, \cdot)\) n/a 164 1
1470.3.e \(\chi_{1470}(491, \cdot)\) n/a 108 1
1470.3.f \(\chi_{1470}(391, \cdot)\) 1470.3.f.a 8 1
1470.3.f.b 16
1470.3.f.c 16
1470.3.f.d 16
1470.3.h \(\chi_{1470}(979, \cdot)\) 1470.3.h.a 32 1
1470.3.h.b 48
1470.3.k \(\chi_{1470}(293, \cdot)\) n/a 320 2
1470.3.l \(\chi_{1470}(883, \cdot)\) n/a 164 2
1470.3.o \(\chi_{1470}(31, \cdot)\) n/a 104 2
1470.3.p \(\chi_{1470}(19, \cdot)\) n/a 160 2
1470.3.q \(\chi_{1470}(569, \cdot)\) n/a 320 2
1470.3.s \(\chi_{1470}(851, \cdot)\) n/a 216 2
1470.3.w \(\chi_{1470}(67, \cdot)\) n/a 320 4
1470.3.x \(\chi_{1470}(227, \cdot)\) n/a 640 4
1470.3.z \(\chi_{1470}(139, \cdot)\) n/a 672 6
1470.3.ba \(\chi_{1470}(181, \cdot)\) n/a 432 6
1470.3.bd \(\chi_{1470}(71, \cdot)\) n/a 912 6
1470.3.bf \(\chi_{1470}(29, \cdot)\) n/a 1344 6
1470.3.bh \(\chi_{1470}(43, \cdot)\) n/a 1344 12
1470.3.bk \(\chi_{1470}(83, \cdot)\) n/a 2688 12
1470.3.bl \(\chi_{1470}(11, \cdot)\) n/a 1776 12
1470.3.bn \(\chi_{1470}(149, \cdot)\) n/a 2688 12
1470.3.bp \(\chi_{1470}(199, \cdot)\) n/a 1344 12
1470.3.br \(\chi_{1470}(61, \cdot)\) n/a 912 12
1470.3.bs \(\chi_{1470}(17, \cdot)\) n/a 5376 24
1470.3.bv \(\chi_{1470}(37, \cdot)\) n/a 2688 24

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1470))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1470)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 2}\)