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Properties

Label 3020.2
Level 3020
Weight 2
Dimension 145394
Nonzero newspaces 36
Sturm bound 1094400
Trace bound 11

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Defining parameters

Level: \( N \) = \( 3020 = 2^{2} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(1094400\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3020))\).

Total New Old
Modular forms 276600 147178 129422
Cusp forms 270601 145394 125207
Eisenstein series 5999 1784 4215

Trace form

\( 145394 q - 146 q^{2} + 4 q^{3} - 150 q^{4} - 440 q^{5} - 450 q^{6} - 4 q^{7} - 158 q^{8} - 302 q^{9} + O(q^{10}) \) \( 145394 q - 146 q^{2} + 4 q^{3} - 150 q^{4} - 440 q^{5} - 450 q^{6} - 4 q^{7} - 158 q^{8} - 302 q^{9} - 237 q^{10} - 150 q^{12} - 300 q^{13} - 150 q^{14} - 4 q^{15} - 434 q^{16} - 300 q^{17} - 138 q^{18} + 8 q^{19} - 217 q^{20} - 892 q^{21} - 150 q^{22} - 12 q^{23} - 150 q^{24} - 464 q^{25} - 458 q^{26} - 8 q^{27} - 150 q^{28} - 312 q^{29} - 225 q^{30} + 8 q^{31} - 166 q^{32} - 300 q^{33} - 150 q^{34} + 4 q^{35} - 474 q^{36} - 276 q^{37} - 150 q^{38} + 8 q^{39} - 217 q^{40} - 880 q^{41} - 150 q^{42} + 20 q^{43} - 150 q^{44} - 460 q^{45} - 450 q^{46} + 12 q^{47} - 150 q^{48} - 294 q^{49} - 197 q^{50} - 24 q^{51} - 142 q^{52} - 324 q^{53} - 150 q^{54} - 450 q^{56} - 316 q^{57} - 166 q^{58} - 24 q^{59} - 225 q^{60} - 952 q^{61} - 150 q^{62} - 4 q^{63} - 150 q^{64} - 450 q^{65} - 450 q^{66} - 4 q^{67} - 126 q^{68} - 276 q^{69} - 225 q^{70} + 24 q^{71} - 126 q^{72} - 260 q^{73} - 150 q^{74} + 4 q^{75} - 450 q^{76} - 300 q^{77} - 150 q^{78} - 16 q^{79} - 257 q^{80} - 842 q^{81} - 182 q^{82} - 12 q^{83} - 150 q^{84} - 426 q^{85} - 450 q^{86} + 24 q^{87} - 150 q^{88} - 288 q^{89} - 237 q^{90} - 8 q^{91} - 150 q^{92} - 316 q^{93} - 150 q^{94} - 8 q^{95} - 450 q^{96} - 356 q^{97} - 178 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3020))\)

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
3020.2.a \(\chi_{3020}(1, \cdot)\) 3020.2.a.a 1 1
3020.2.a.b 1
3020.2.a.c 1
3020.2.a.d 4
3020.2.a.e 4
3020.2.a.f 6
3020.2.a.g 8
3020.2.a.h 10
3020.2.a.i 15
3020.2.b \(\chi_{3020}(3019, \cdot)\) n/a 452 1
3020.2.d \(\chi_{3020}(1209, \cdot)\) 3020.2.d.a 2 1
3020.2.d.b 2
3020.2.d.c 2
3020.2.d.d 4
3020.2.d.e 28
3020.2.d.f 38
3020.2.g \(\chi_{3020}(1811, \cdot)\) n/a 304 1
3020.2.i \(\chi_{3020}(2081, \cdot)\) 3020.2.i.a 2 2
3020.2.i.b 48
3020.2.i.c 50
3020.2.k \(\chi_{3020}(303, \cdot)\) n/a 900 2
3020.2.l \(\chi_{3020}(2113, \cdot)\) n/a 152 2
3020.2.n \(\chi_{3020}(321, \cdot)\) n/a 208 4
3020.2.p \(\chi_{3020}(269, \cdot)\) n/a 152 2
3020.2.r \(\chi_{3020}(119, \cdot)\) n/a 904 2
3020.2.t \(\chi_{3020}(1931, \cdot)\) n/a 608 2
3020.2.w \(\chi_{3020}(691, \cdot)\) n/a 1216 4
3020.2.z \(\chi_{3020}(1529, \cdot)\) n/a 304 4
3020.2.bb \(\chi_{3020}(1899, \cdot)\) n/a 1808 4
3020.2.bc \(\chi_{3020}(33, \cdot)\) n/a 304 4
3020.2.bf \(\chi_{3020}(183, \cdot)\) n/a 1808 4
3020.2.bg \(\chi_{3020}(581, \cdot)\) n/a 400 8
3020.2.bi \(\chi_{3020}(993, \cdot)\) n/a 608 8
3020.2.bj \(\chi_{3020}(623, \cdot)\) n/a 3616 8
3020.2.bl \(\chi_{3020}(81, \cdot)\) n/a 1040 20
3020.2.bn \(\chi_{3020}(451, \cdot)\) n/a 2432 8
3020.2.bp \(\chi_{3020}(499, \cdot)\) n/a 3616 8
3020.2.br \(\chi_{3020}(189, \cdot)\) n/a 608 8
3020.2.bv \(\chi_{3020}(9, \cdot)\) n/a 1520 20
3020.2.bx \(\chi_{3020}(131, \cdot)\) n/a 6080 20
3020.2.bz \(\chi_{3020}(79, \cdot)\) n/a 9040 20
3020.2.ca \(\chi_{3020}(167, \cdot)\) n/a 7232 16
3020.2.cd \(\chi_{3020}(113, \cdot)\) n/a 1216 16
3020.2.ce \(\chi_{3020}(21, \cdot)\) n/a 2000 40
3020.2.cg \(\chi_{3020}(123, \cdot)\) n/a 18080 40
3020.2.ci \(\chi_{3020}(53, \cdot)\) n/a 3040 40
3020.2.cj \(\chi_{3020}(49, \cdot)\) n/a 3040 40
3020.2.cm \(\chi_{3020}(199, \cdot)\) n/a 18080 40
3020.2.co \(\chi_{3020}(51, \cdot)\) n/a 12160 40
3020.2.cq \(\chi_{3020}(43, \cdot)\) n/a 36160 80
3020.2.cs \(\chi_{3020}(13, \cdot)\) n/a 6080 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3020))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3020)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(302))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(604))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(755))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1510))\)\(^{\oplus 2}\)