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Properties

Label 3042.3
Level 3042
Weight 3
Dimension 133272
Nonzero newspaces 30
Sturm bound 1533168
Trace bound 11

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Defining parameters

Level: \( N \) = \( 3042 = 2 \cdot 3^{2} \cdot 13^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(1533168\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(3042))\).

Total New Old
Modular forms 514704 133272 381432
Cusp forms 507408 133272 374136
Eisenstein series 7296 0 7296

Trace form

\( 133272 q - 18 q^{5} - 12 q^{6} + 34 q^{7} + 24 q^{8} + 12 q^{9} + O(q^{10}) \) \( 133272 q - 18 q^{5} - 12 q^{6} + 34 q^{7} + 24 q^{8} + 12 q^{9} + 72 q^{10} + 42 q^{11} + 12 q^{12} - 24 q^{13} - 12 q^{14} + 18 q^{15} - 32 q^{16} - 72 q^{17} - 24 q^{18} - 152 q^{19} - 84 q^{20} - 42 q^{21} - 60 q^{22} + 66 q^{23} + 18 q^{25} - 216 q^{28} - 1398 q^{29} - 696 q^{30} - 1194 q^{31} - 666 q^{33} - 516 q^{34} - 1320 q^{35} - 180 q^{36} - 180 q^{37} - 72 q^{38} + 96 q^{39} - 24 q^{40} + 798 q^{41} + 528 q^{42} + 970 q^{43} + 864 q^{44} + 1626 q^{45} + 1176 q^{46} + 2094 q^{47} + 24 q^{48} + 1786 q^{49} + 1812 q^{50} + 1176 q^{51} + 204 q^{52} + 480 q^{53} + 36 q^{54} + 492 q^{55} + 264 q^{56} + 144 q^{57} + 336 q^{58} + 294 q^{59} - 36 q^{60} + 6 q^{61} + 144 q^{62} - 1122 q^{63} - 48 q^{64} - 1386 q^{65} - 72 q^{66} - 1946 q^{67} + 48 q^{68} - 1134 q^{69} - 588 q^{70} - 2064 q^{71} - 96 q^{72} - 1904 q^{73} - 84 q^{74} - 492 q^{75} + 184 q^{76} - 90 q^{77} + 486 q^{79} - 96 q^{80} + 516 q^{81} + 672 q^{82} + 2286 q^{83} - 144 q^{84} + 3132 q^{85} + 84 q^{86} + 1866 q^{87} + 120 q^{88} + 3024 q^{89} + 956 q^{91} - 60 q^{92} + 2526 q^{93} - 156 q^{94} + 2292 q^{95} + 48 q^{96} - 1410 q^{97} + 2208 q^{98} + 5022 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(3042))\)

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
3042.3.c \(\chi_{3042}(1691, \cdot)\) 3042.3.c.a 2 1
3042.3.c.b 2
3042.3.c.c 2
3042.3.c.d 2
3042.3.c.e 2
3042.3.c.f 2
3042.3.c.g 2
3042.3.c.h 2
3042.3.c.i 2
3042.3.c.j 4
3042.3.c.k 4
3042.3.c.l 6
3042.3.c.m 6
3042.3.c.n 8
3042.3.c.o 8
3042.3.c.p 12
3042.3.c.q 12
3042.3.c.r 12
3042.3.c.s 12
3042.3.d \(\chi_{3042}(3041, \cdot)\) 3042.3.d.a 4 1
3042.3.d.b 4
3042.3.d.c 8
3042.3.d.d 8
3042.3.d.e 12
3042.3.d.f 16
3042.3.d.g 24
3042.3.d.h 24
3042.3.i \(\chi_{3042}(577, \cdot)\) n/a 254 2
3042.3.k \(\chi_{3042}(1205, \cdot)\) n/a 208 2
3042.3.m \(\chi_{3042}(23, \cdot)\) n/a 616 2
3042.3.n \(\chi_{3042}(1013, \cdot)\) n/a 616 2
3042.3.o \(\chi_{3042}(1037, \cdot)\) n/a 616 2
3042.3.q \(\chi_{3042}(1667, \cdot)\) n/a 616 2
3042.3.r \(\chi_{3042}(677, \cdot)\) n/a 620 2
3042.3.u \(\chi_{3042}(191, \cdot)\) n/a 616 2
3042.3.v \(\chi_{3042}(485, \cdot)\) n/a 208 2
3042.3.w \(\chi_{3042}(1591, \cdot)\) n/a 1232 4
3042.3.ba \(\chi_{3042}(427, \cdot)\) n/a 1232 4
3042.3.bb \(\chi_{3042}(19, \cdot)\) n/a 516 4
3042.3.bc \(\chi_{3042}(319, \cdot)\) n/a 1232 4
3042.3.bf \(\chi_{3042}(233, \cdot)\) n/a 1488 12
3042.3.bg \(\chi_{3042}(53, \cdot)\) n/a 1488 12
3042.3.bn \(\chi_{3042}(73, \cdot)\) n/a 3672 24
3042.3.bo \(\chi_{3042}(17, \cdot)\) n/a 2880 24
3042.3.bp \(\chi_{3042}(185, \cdot)\) n/a 8736 24
3042.3.bs \(\chi_{3042}(131, \cdot)\) n/a 8736 24
3042.3.bt \(\chi_{3042}(29, \cdot)\) n/a 8736 24
3042.3.bv \(\chi_{3042}(95, \cdot)\) n/a 8736 24
3042.3.bw \(\chi_{3042}(77, \cdot)\) n/a 8736 24
3042.3.bx \(\chi_{3042}(173, \cdot)\) n/a 8736 24
3042.3.bz \(\chi_{3042}(35, \cdot)\) n/a 2880 24
3042.3.cb \(\chi_{3042}(7, \cdot)\) n/a 17472 48
3042.3.cc \(\chi_{3042}(85, \cdot)\) n/a 17472 48
3042.3.cd \(\chi_{3042}(37, \cdot)\) n/a 7248 48
3042.3.ch \(\chi_{3042}(31, \cdot)\) n/a 17472 48

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(3042))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(3042)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1014))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(1521))\)\(^{\oplus 2}\)