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Properties

Label 1470.4
Level 1470
Weight 4
Dimension 37240
Nonzero newspaces 24
Sturm bound 451584
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(451584\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1470))\).

Total New Old
Modular forms 171264 37240 134024
Cusp forms 167424 37240 130184
Eisenstein series 3840 0 3840

Trace form

\( 37240 q - 34 q^{3} + 100 q^{5} + 140 q^{6} + 192 q^{7} - 168 q^{9} + O(q^{10}) \) \( 37240 q - 34 q^{3} + 100 q^{5} + 140 q^{6} + 192 q^{7} - 168 q^{9} - 184 q^{10} - 304 q^{11} - 200 q^{12} - 104 q^{13} + 266 q^{15} - 128 q^{16} - 24 q^{17} - 688 q^{18} - 1520 q^{19} - 16 q^{20} - 1296 q^{21} + 336 q^{22} + 408 q^{23} - 144 q^{24} + 4856 q^{25} + 2112 q^{26} + 2750 q^{27} + 192 q^{28} - 600 q^{29} - 588 q^{30} - 1200 q^{31} - 1960 q^{33} - 3488 q^{34} - 4020 q^{35} + 704 q^{36} + 8968 q^{37} + 5760 q^{38} + 1068 q^{39} + 1344 q^{40} + 2312 q^{41} - 72 q^{42} - 1016 q^{43} - 1664 q^{44} + 2632 q^{45} - 11824 q^{46} - 5328 q^{47} - 992 q^{48} - 24456 q^{49} - 3488 q^{50} - 1340 q^{51} + 1216 q^{52} - 4224 q^{53} + 828 q^{54} + 9712 q^{55} + 1152 q^{56} + 6152 q^{57} + 6720 q^{58} + 20456 q^{59} + 1664 q^{60} + 13040 q^{61} + 10656 q^{62} - 5460 q^{63} - 3072 q^{64} - 14448 q^{65} - 7888 q^{66} - 21848 q^{67} - 96 q^{68} - 7008 q^{69} + 1008 q^{70} + 672 q^{71} + 2752 q^{72} + 2176 q^{73} - 1936 q^{74} + 4306 q^{75} + 1024 q^{76} - 2088 q^{77} + 8616 q^{78} + 14056 q^{79} + 1600 q^{80} + 25912 q^{81} + 9216 q^{82} + 46608 q^{83} + 1824 q^{84} + 37288 q^{85} + 6160 q^{86} + 572 q^{87} - 1344 q^{88} + 4624 q^{89} - 12808 q^{90} - 16128 q^{91} + 8736 q^{92} - 38608 q^{93} + 10112 q^{94} - 22680 q^{95} + 448 q^{96} - 19976 q^{97} + 1632 q^{98} - 6744 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1470))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1470.4.a \(\chi_{1470}(1, \cdot)\) 1470.4.a.a 1 1
1470.4.a.b 1
1470.4.a.c 1
1470.4.a.d 1
1470.4.a.e 1
1470.4.a.f 1
1470.4.a.g 1
1470.4.a.h 1
1470.4.a.i 1
1470.4.a.j 1
1470.4.a.k 1
1470.4.a.l 1
1470.4.a.m 1
1470.4.a.n 1
1470.4.a.o 1
1470.4.a.p 1
1470.4.a.q 1
1470.4.a.r 1
1470.4.a.s 1
1470.4.a.t 1
1470.4.a.u 1
1470.4.a.v 1
1470.4.a.w 1
1470.4.a.x 1
1470.4.a.y 1
1470.4.a.z 1
1470.4.a.ba 1
1470.4.a.bb 1
1470.4.a.bc 1
1470.4.a.bd 1
1470.4.a.be 2
1470.4.a.bf 2
1470.4.a.bg 2
1470.4.a.bh 2
1470.4.a.bi 2
1470.4.a.bj 2
1470.4.a.bk 2
1470.4.a.bl 2
1470.4.a.bm 2
1470.4.a.bn 2
1470.4.a.bo 2
1470.4.a.bp 2
1470.4.a.bq 2
1470.4.a.br 2
1470.4.a.bs 2
1470.4.a.bt 3
1470.4.a.bu 3
1470.4.a.bv 4
1470.4.a.bw 4
1470.4.a.bx 4
1470.4.a.by 4
1470.4.b \(\chi_{1470}(881, \cdot)\) n/a 160 1
1470.4.d \(\chi_{1470}(1469, \cdot)\) n/a 240 1
1470.4.g \(\chi_{1470}(589, \cdot)\) n/a 122 1
1470.4.i \(\chi_{1470}(361, \cdot)\) n/a 160 2
1470.4.j \(\chi_{1470}(197, \cdot)\) n/a 492 2
1470.4.m \(\chi_{1470}(97, \cdot)\) n/a 240 2
1470.4.n \(\chi_{1470}(79, \cdot)\) n/a 240 2
1470.4.r \(\chi_{1470}(521, \cdot)\) n/a 320 2
1470.4.t \(\chi_{1470}(509, \cdot)\) n/a 480 2
1470.4.u \(\chi_{1470}(211, \cdot)\) n/a 672 6
1470.4.v \(\chi_{1470}(313, \cdot)\) n/a 480 4
1470.4.y \(\chi_{1470}(263, \cdot)\) n/a 960 4
1470.4.bb \(\chi_{1470}(169, \cdot)\) n/a 1008 6
1470.4.bc \(\chi_{1470}(209, \cdot)\) n/a 2016 6
1470.4.be \(\chi_{1470}(41, \cdot)\) n/a 1344 6
1470.4.bg \(\chi_{1470}(121, \cdot)\) n/a 1344 12
1470.4.bi \(\chi_{1470}(13, \cdot)\) n/a 2016 12
1470.4.bj \(\chi_{1470}(113, \cdot)\) n/a 4032 12
1470.4.bm \(\chi_{1470}(59, \cdot)\) n/a 4032 12
1470.4.bo \(\chi_{1470}(101, \cdot)\) n/a 2688 12
1470.4.bq \(\chi_{1470}(109, \cdot)\) n/a 2016 12
1470.4.bt \(\chi_{1470}(23, \cdot)\) n/a 8064 24
1470.4.bu \(\chi_{1470}(73, \cdot)\) n/a 4032 24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1470))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1470)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 2}\)