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Properties

Label 2070.3
Level 2070
Weight 3
Dimension 54972
Nonzero newspaces 24
Sturm bound 684288
Trace bound 4

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Defining parameters

Level: \( N \) = \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(684288\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(2070))\).

Total New Old
Modular forms 230912 54972 175940
Cusp forms 225280 54972 170308
Eisenstein series 5632 0 5632

Trace form

\( 54972 q + 4 q^{2} - 36 q^{5} - 48 q^{6} - 32 q^{7} - 8 q^{8} - 32 q^{9} + O(q^{10}) \) \( 54972 q + 4 q^{2} - 36 q^{5} - 48 q^{6} - 32 q^{7} - 8 q^{8} - 32 q^{9} - 84 q^{10} - 88 q^{11} + 16 q^{12} - 52 q^{13} + 144 q^{14} + 84 q^{15} + 16 q^{16} + 480 q^{17} + 32 q^{18} + 164 q^{19} + 124 q^{20} - 72 q^{21} - 16 q^{22} - 96 q^{23} - 252 q^{25} - 152 q^{26} - 96 q^{27} - 152 q^{28} - 236 q^{29} + 144 q^{30} + 28 q^{31} - 16 q^{32} + 760 q^{33} + 80 q^{34} + 1188 q^{35} + 304 q^{36} + 796 q^{37} + 80 q^{38} + 712 q^{39} - 72 q^{40} + 280 q^{41} + 64 q^{42} - 224 q^{43} - 268 q^{45} + 136 q^{46} - 512 q^{47} - 32 q^{48} - 840 q^{49} - 484 q^{50} - 1440 q^{51} + 56 q^{52} - 1476 q^{53} - 2048 q^{54} - 1284 q^{55} - 1520 q^{56} - 3640 q^{57} - 2528 q^{58} - 5584 q^{59} - 648 q^{60} - 4520 q^{61} - 3320 q^{62} - 2000 q^{63} - 192 q^{64} - 2202 q^{65} - 1760 q^{66} - 1256 q^{67} - 232 q^{68} + 276 q^{69} - 216 q^{70} + 1900 q^{71} + 320 q^{72} + 612 q^{73} + 3456 q^{74} + 4160 q^{75} + 192 q^{76} + 7180 q^{77} + 3536 q^{78} + 5624 q^{79} + 792 q^{80} + 5712 q^{81} + 4736 q^{82} + 7204 q^{83} + 1312 q^{84} + 3196 q^{85} + 3336 q^{86} + 328 q^{87} + 32 q^{88} + 88 q^{89} - 128 q^{90} + 1984 q^{91} - 16 q^{92} - 808 q^{93} + 16 q^{94} - 3454 q^{95} + 64 q^{96} - 1240 q^{97} - 2396 q^{98} - 1736 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(2070))\)

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
2070.3.b \(\chi_{2070}(1979, \cdot)\) 2070.3.b.a 88 1
2070.3.c \(\chi_{2070}(91, \cdot)\) 2070.3.c.a 16 1
2070.3.c.b 32
2070.3.c.c 32
2070.3.f \(\chi_{2070}(919, \cdot)\) n/a 120 1
2070.3.g \(\chi_{2070}(1151, \cdot)\) 2070.3.g.a 32 1
2070.3.g.b 32
2070.3.l \(\chi_{2070}(1243, \cdot)\) n/a 220 2
2070.3.m \(\chi_{2070}(413, \cdot)\) n/a 192 2
2070.3.o \(\chi_{2070}(461, \cdot)\) n/a 352 2
2070.3.p \(\chi_{2070}(229, \cdot)\) n/a 576 2
2070.3.s \(\chi_{2070}(781, \cdot)\) n/a 384 2
2070.3.t \(\chi_{2070}(599, \cdot)\) n/a 528 2
2070.3.v \(\chi_{2070}(277, \cdot)\) n/a 1056 4
2070.3.w \(\chi_{2070}(137, \cdot)\) n/a 1152 4
2070.3.ba \(\chi_{2070}(71, \cdot)\) n/a 640 10
2070.3.bb \(\chi_{2070}(19, \cdot)\) n/a 1200 10
2070.3.be \(\chi_{2070}(181, \cdot)\) n/a 800 10
2070.3.bf \(\chi_{2070}(179, \cdot)\) n/a 960 10
2070.3.bh \(\chi_{2070}(17, \cdot)\) n/a 1920 20
2070.3.bi \(\chi_{2070}(73, \cdot)\) n/a 2400 20
2070.3.bl \(\chi_{2070}(29, \cdot)\) n/a 5760 20
2070.3.bm \(\chi_{2070}(61, \cdot)\) n/a 3840 20
2070.3.bp \(\chi_{2070}(79, \cdot)\) n/a 5760 20
2070.3.bq \(\chi_{2070}(41, \cdot)\) n/a 3840 20
2070.3.bu \(\chi_{2070}(83, \cdot)\) n/a 11520 40
2070.3.bv \(\chi_{2070}(13, \cdot)\) n/a 11520 40

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(2070))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(2070)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1035))\)\(^{\oplus 2}\)