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Properties

Label 3002.2
Level 3002
Weight 2
Dimension 93053
Nonzero newspaces 32
Sturm bound 1123200
Trace bound 19

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Defining parameters

Level: \( N \) = \( 3002 = 2 \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(1123200\)
Trace bound: \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3002))\).

Total New Old
Modular forms 283608 93053 190555
Cusp forms 277993 93053 184940
Eisenstein series 5615 0 5615

Trace form

\( 93053 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 12 q^{6} + 24 q^{7} + 3 q^{8} + 39 q^{9} + O(q^{10}) \) \( 93053 q + 3 q^{2} + 12 q^{3} + 3 q^{4} + 18 q^{5} + 12 q^{6} + 24 q^{7} + 3 q^{8} + 39 q^{9} + 18 q^{10} + 36 q^{11} - 6 q^{13} - 12 q^{14} + 3 q^{16} + 18 q^{17} - 15 q^{18} - 45 q^{19} - 18 q^{20} + 12 q^{21} - 18 q^{22} + 36 q^{23} + 12 q^{24} + 21 q^{25} + 6 q^{26} + 54 q^{27} + 12 q^{28} + 54 q^{29} + 72 q^{30} + 60 q^{31} + 3 q^{32} + 36 q^{33} + 54 q^{34} + 72 q^{35} + 39 q^{36} + 78 q^{37} + 39 q^{38} + 60 q^{39} + 18 q^{40} + 90 q^{41} + 96 q^{42} + 48 q^{43} + 18 q^{44} + 18 q^{45} - 6 q^{48} + 51 q^{49} - 51 q^{50} + 18 q^{51} + 30 q^{52} + 18 q^{53} + 12 q^{54} + 72 q^{55} - 48 q^{56} - 24 q^{57} + 18 q^{58} + 30 q^{61} - 12 q^{62} - 88 q^{63} - 9 q^{64} - 276 q^{65} - 312 q^{66} - 316 q^{67} - 120 q^{68} - 444 q^{69} - 552 q^{70} - 240 q^{71} + 21 q^{72} - 156 q^{73} - 198 q^{74} - 336 q^{75} - 143 q^{76} - 252 q^{77} - 216 q^{78} - 855 q^{79} + 18 q^{80} - 771 q^{81} - 258 q^{82} - 360 q^{83} - 376 q^{84} - 444 q^{85} - 252 q^{86} - 312 q^{87} + 36 q^{88} - 186 q^{89} - 570 q^{90} - 480 q^{91} - 156 q^{92} - 280 q^{93} - 312 q^{94} - 102 q^{95} + 12 q^{96} - 94 q^{97} + 27 q^{98} + 54 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3002))\)

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
3002.2.a \(\chi_{3002}(1, \cdot)\) 3002.2.a.a 1 1
3002.2.a.b 1
3002.2.a.c 1
3002.2.a.d 1
3002.2.a.e 2
3002.2.a.f 4
3002.2.a.g 8
3002.2.a.h 9
3002.2.a.i 11
3002.2.a.j 13
3002.2.a.k 13
3002.2.a.l 16
3002.2.a.m 16
3002.2.a.n 21
3002.2.d \(\chi_{3002}(3001, \cdot)\) n/a 136 1
3002.2.e \(\chi_{3002}(1445, \cdot)\) n/a 240 2
3002.2.f \(\chi_{3002}(159, \cdot)\) n/a 260 2
3002.2.g \(\chi_{3002}(1603, \cdot)\) n/a 264 2
3002.2.h \(\chi_{3002}(1793, \cdot)\) n/a 264 2
3002.2.k \(\chi_{3002}(1737, \cdot)\) n/a 272 2
3002.2.l \(\chi_{3002}(1367, \cdot)\) n/a 264 2
3002.2.m \(\chi_{3002}(103, \cdot)\) n/a 264 2
3002.2.t \(\chi_{3002}(293, \cdot)\) n/a 264 2
3002.2.u \(\chi_{3002}(633, \cdot)\) n/a 780 6
3002.2.v \(\chi_{3002}(23, \cdot)\) n/a 804 6
3002.2.w \(\chi_{3002}(213, \cdot)\) n/a 804 6
3002.2.x \(\chi_{3002}(381, \cdot)\) n/a 1440 12
3002.2.y \(\chi_{3002}(135, \cdot)\) n/a 804 6
3002.2.bc \(\chi_{3002}(789, \cdot)\) n/a 792 6
3002.2.be \(\chi_{3002}(261, \cdot)\) n/a 804 6
3002.2.bh \(\chi_{3002}(227, \cdot)\) n/a 1632 12
3002.2.bk \(\chi_{3002}(11, \cdot)\) n/a 3168 24
3002.2.bl \(\chi_{3002}(49, \cdot)\) n/a 3168 24
3002.2.bm \(\chi_{3002}(87, \cdot)\) n/a 3264 24
3002.2.bn \(\chi_{3002}(115, \cdot)\) n/a 2880 24
3002.2.bo \(\chi_{3002}(107, \cdot)\) n/a 3168 24
3002.2.bv \(\chi_{3002}(217, \cdot)\) n/a 3168 24
3002.2.bw \(\chi_{3002}(37, \cdot)\) n/a 3168 24
3002.2.bx \(\chi_{3002}(27, \cdot)\) n/a 3264 24
3002.2.ca \(\chi_{3002}(5, \cdot)\) n/a 9648 72
3002.2.cb \(\chi_{3002}(9, \cdot)\) n/a 9648 72
3002.2.cc \(\chi_{3002}(101, \cdot)\) n/a 9504 72
3002.2.cf \(\chi_{3002}(3, \cdot)\) n/a 9648 72
3002.2.ch \(\chi_{3002}(15, \cdot)\) n/a 9504 72
3002.2.cl \(\chi_{3002}(147, \cdot)\) n/a 9648 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3002))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(158))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1501))\)\(^{\oplus 2}\)