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Properties

Label 3468.2
Level 3468
Weight 2
Dimension 143912
Nonzero newspaces 20
Sturm bound 1331712
Trace bound 7

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Defining parameters

Level: \( N \) = \( 3468 = 2^{2} \cdot 3 \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(1331712\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3468))\).

Total New Old
Modular forms 336928 145388 191540
Cusp forms 328929 143912 185017
Eisenstein series 7999 1476 6523

Trace form

\( 143912 q - 240 q^{4} - 120 q^{6} - 240 q^{9} + O(q^{10}) \) \( 143912 q - 240 q^{4} - 120 q^{6} - 240 q^{9} - 240 q^{10} - 32 q^{11} - 120 q^{12} - 512 q^{13} - 48 q^{15} - 208 q^{16} - 16 q^{17} - 232 q^{18} - 32 q^{19} - 288 q^{21} - 240 q^{22} - 32 q^{23} - 88 q^{24} - 432 q^{25} + 128 q^{26} - 48 q^{28} + 80 q^{29} + 8 q^{30} + 128 q^{31} + 160 q^{32} - 144 q^{33} - 128 q^{34} + 128 q^{35} - 88 q^{36} - 352 q^{37} + 160 q^{38} + 96 q^{39} + 16 q^{40} + 80 q^{41} - 24 q^{42} + 96 q^{43} + 128 q^{44} - 160 q^{45} - 176 q^{46} - 168 q^{48} - 480 q^{49} + 32 q^{51} - 464 q^{52} + 48 q^{53} - 200 q^{54} + 64 q^{55} - 160 q^{56} + 16 q^{57} - 464 q^{58} + 64 q^{59} - 328 q^{60} - 288 q^{61} - 224 q^{62} + 144 q^{63} - 432 q^{64} + 432 q^{65} - 360 q^{66} + 64 q^{67} - 176 q^{68} - 304 q^{69} - 528 q^{70} - 328 q^{72} - 208 q^{73} - 192 q^{74} + 32 q^{75} - 464 q^{76} + 64 q^{77} - 328 q^{78} - 64 q^{79} - 224 q^{80} - 64 q^{81} - 400 q^{82} - 32 q^{83} - 264 q^{84} - 584 q^{85} - 192 q^{87} - 240 q^{88} - 96 q^{89} - 440 q^{90} - 192 q^{91} - 432 q^{93} - 240 q^{94} - 128 q^{95} - 424 q^{96} - 608 q^{97} - 208 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3468))\)

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
3468.2.a \(\chi_{3468}(1, \cdot)\) 3468.2.a.a 1 1
3468.2.a.b 1
3468.2.a.c 1
3468.2.a.d 1
3468.2.a.e 1
3468.2.a.f 1
3468.2.a.g 1
3468.2.a.h 1
3468.2.a.i 2
3468.2.a.j 2
3468.2.a.k 3
3468.2.a.l 3
3468.2.a.m 6
3468.2.a.n 6
3468.2.a.o 8
3468.2.a.p 8
3468.2.b \(\chi_{3468}(577, \cdot)\) 3468.2.b.a 2 1
3468.2.b.b 2
3468.2.b.c 2
3468.2.b.d 2
3468.2.b.e 4
3468.2.b.f 6
3468.2.b.g 12
3468.2.b.h 16
3468.2.c \(\chi_{3468}(2891, \cdot)\) n/a 512 1
3468.2.h \(\chi_{3468}(3467, \cdot)\) n/a 512 1
3468.2.j \(\chi_{3468}(829, \cdot)\) 3468.2.j.a 4 2
3468.2.j.b 4
3468.2.j.c 4
3468.2.j.d 4
3468.2.j.e 4
3468.2.j.f 4
3468.2.j.g 12
3468.2.j.h 16
3468.2.j.i 16
3468.2.j.j 24
3468.2.l \(\chi_{3468}(251, \cdot)\) n/a 1024 2
3468.2.o \(\chi_{3468}(733, \cdot)\) n/a 176 4
3468.2.p \(\chi_{3468}(155, \cdot)\) n/a 2048 4
3468.2.q \(\chi_{3468}(65, \cdot)\) n/a 720 8
3468.2.r \(\chi_{3468}(643, \cdot)\) n/a 2160 8
3468.2.u \(\chi_{3468}(205, \cdot)\) n/a 800 16
3468.2.v \(\chi_{3468}(203, \cdot)\) n/a 9728 16
3468.2.ba \(\chi_{3468}(35, \cdot)\) n/a 9728 16
3468.2.bb \(\chi_{3468}(169, \cdot)\) n/a 800 16
3468.2.bc \(\chi_{3468}(47, \cdot)\) n/a 19456 32
3468.2.be \(\chi_{3468}(13, \cdot)\) n/a 1600 32
3468.2.bg \(\chi_{3468}(59, \cdot)\) n/a 38912 64
3468.2.bh \(\chi_{3468}(25, \cdot)\) n/a 3328 64
3468.2.bm \(\chi_{3468}(7, \cdot)\) n/a 39168 128
3468.2.bn \(\chi_{3468}(5, \cdot)\) n/a 13056 128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3468))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3468)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1734))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3468))\)\(^{\oplus 1}\)