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Properties

Label 3042.2
Level 3042
Weight 2
Dimension 66635
Nonzero newspaces 30
Sturm bound 1022112
Trace bound 11

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Defining parameters

Level: \( N \) = \( 3042 = 2 \cdot 3^{2} \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(1022112\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3042))\).

Total New Old
Modular forms 259176 66635 192541
Cusp forms 251881 66635 185246
Eisenstein series 7295 0 7295

Trace form

\( 66635 q - q^{2} - 3 q^{3} - q^{4} + 3 q^{6} - 10 q^{7} - 4 q^{8} + 3 q^{9} + O(q^{10}) \) \( 66635 q - q^{2} - 3 q^{3} - q^{4} + 3 q^{6} - 10 q^{7} - 4 q^{8} + 3 q^{9} - 30 q^{10} - 21 q^{11} - 24 q^{13} - 26 q^{14} - 9 q^{16} - 36 q^{17} - 6 q^{18} - 58 q^{19} - 6 q^{20} + 6 q^{21} + 3 q^{22} - 18 q^{23} - 3 q^{24} - 25 q^{25} + 28 q^{28} + 108 q^{29} + 96 q^{30} + 148 q^{31} - q^{32} + 135 q^{33} + 147 q^{34} + 336 q^{35} + 99 q^{36} + 154 q^{37} + 217 q^{38} + 96 q^{39} + 273 q^{41} + 144 q^{42} + 137 q^{43} + 138 q^{44} + 240 q^{45} + 132 q^{46} + 198 q^{47} + 3 q^{48} + 163 q^{49} + 143 q^{50} + 105 q^{51} + 9 q^{52} - 48 q^{53} + 9 q^{54} - 120 q^{55} - 26 q^{56} + 3 q^{57} - 60 q^{58} - 99 q^{59} - 86 q^{61} - 80 q^{62} + 84 q^{63} - 4 q^{64} + 57 q^{65} + 35 q^{67} - 3 q^{68} + 144 q^{69} - 72 q^{70} + 216 q^{71} + 3 q^{72} + 230 q^{73} - 74 q^{74} + 225 q^{75} - 55 q^{76} + 150 q^{77} + 4 q^{79} - 6 q^{80} + 183 q^{81} - 84 q^{82} + 276 q^{83} - 6 q^{84} + 138 q^{85} - 47 q^{86} + 210 q^{87} + 3 q^{88} + 108 q^{89} + 20 q^{91} - 42 q^{92} + 144 q^{93} - 114 q^{94} + 48 q^{95} - 125 q^{97} - 198 q^{98} - 270 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3042))\)

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
3042.2.a \(\chi_{3042}(1, \cdot)\) 3042.2.a.a 1 1
3042.2.a.b 1
3042.2.a.c 1
3042.2.a.d 1
3042.2.a.e 1
3042.2.a.f 1
3042.2.a.g 1
3042.2.a.h 1
3042.2.a.i 1
3042.2.a.j 1
3042.2.a.k 1
3042.2.a.l 1
3042.2.a.m 1
3042.2.a.n 1
3042.2.a.o 1
3042.2.a.p 2
3042.2.a.q 2
3042.2.a.r 2
3042.2.a.s 2
3042.2.a.t 2
3042.2.a.u 2
3042.2.a.v 2
3042.2.a.w 2
3042.2.a.x 2
3042.2.a.y 2
3042.2.a.z 3
3042.2.a.ba 3
3042.2.a.bb 3
3042.2.a.bc 3
3042.2.a.bd 3
3042.2.a.be 3
3042.2.a.bf 3
3042.2.a.bg 3
3042.2.a.bh 3
3042.2.a.bi 3
3042.2.b \(\chi_{3042}(1351, \cdot)\) 3042.2.b.a 2 1
3042.2.b.b 2
3042.2.b.c 2
3042.2.b.d 2
3042.2.b.e 2
3042.2.b.f 2
3042.2.b.g 2
3042.2.b.h 2
3042.2.b.i 4
3042.2.b.j 4
3042.2.b.k 4
3042.2.b.l 4
3042.2.b.m 4
3042.2.b.n 6
3042.2.b.o 6
3042.2.b.p 6
3042.2.b.q 6
3042.2.b.r 6
3042.2.e \(\chi_{3042}(1015, \cdot)\) n/a 310 2
3042.2.f \(\chi_{3042}(1543, \cdot)\) n/a 308 2
3042.2.g \(\chi_{3042}(529, \cdot)\) n/a 308 2
3042.2.h \(\chi_{3042}(991, \cdot)\) n/a 126 2
3042.2.j \(\chi_{3042}(2267, \cdot)\) n/a 108 2
3042.2.l \(\chi_{3042}(361, \cdot)\) n/a 128 2
3042.2.p \(\chi_{3042}(2389, \cdot)\) n/a 308 2
3042.2.s \(\chi_{3042}(823, \cdot)\) n/a 308 2
3042.2.t \(\chi_{3042}(337, \cdot)\) n/a 308 2
3042.2.x \(\chi_{3042}(89, \cdot)\) n/a 200 4
3042.2.y \(\chi_{3042}(587, \cdot)\) n/a 616 4
3042.2.z \(\chi_{3042}(695, \cdot)\) n/a 616 4
3042.2.bd \(\chi_{3042}(239, \cdot)\) n/a 616 4
3042.2.be \(\chi_{3042}(235, \cdot)\) n/a 900 12
3042.2.bh \(\chi_{3042}(181, \cdot)\) n/a 888 12
3042.2.bi \(\chi_{3042}(55, \cdot)\) n/a 1848 24
3042.2.bj \(\chi_{3042}(61, \cdot)\) n/a 4368 24
3042.2.bk \(\chi_{3042}(133, \cdot)\) n/a 4368 24
3042.2.bl \(\chi_{3042}(79, \cdot)\) n/a 4368 24
3042.2.bm \(\chi_{3042}(125, \cdot)\) n/a 1392 24
3042.2.bq \(\chi_{3042}(25, \cdot)\) n/a 4368 24
3042.2.br \(\chi_{3042}(121, \cdot)\) n/a 4368 24
3042.2.bu \(\chi_{3042}(43, \cdot)\) n/a 4368 24
3042.2.by \(\chi_{3042}(127, \cdot)\) n/a 1824 24
3042.2.ca \(\chi_{3042}(5, \cdot)\) n/a 8736 48
3042.2.ce \(\chi_{3042}(11, \cdot)\) n/a 8736 48
3042.2.cf \(\chi_{3042}(71, \cdot)\) n/a 2976 48
3042.2.cg \(\chi_{3042}(41, \cdot)\) n/a 8736 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3042))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3042)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1014))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1521))\)\(^{\oplus 2}\)