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Properties

Label 3249.2
Level 3249
Weight 2
Dimension 304839
Nonzero newspaces 32
Sturm bound 1559520
Trace bound 3

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Defining parameters

Level: \( N \) = \( 3249 = 3^{2} \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(1559520\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3249))\).

Total New Old
Modular forms 393912 309056 84856
Cusp forms 385849 304839 81010
Eisenstein series 8063 4217 3846

Trace form

\( 304839 q - 459 q^{2} - 612 q^{3} - 459 q^{4} - 459 q^{5} - 612 q^{6} - 459 q^{7} - 459 q^{8} - 612 q^{9} + O(q^{10}) \) \( 304839 q - 459 q^{2} - 612 q^{3} - 459 q^{4} - 459 q^{5} - 612 q^{6} - 459 q^{7} - 459 q^{8} - 612 q^{9} - 1377 q^{10} - 459 q^{11} - 612 q^{12} - 435 q^{13} - 423 q^{14} - 612 q^{15} - 387 q^{16} - 441 q^{17} - 612 q^{18} - 1437 q^{19} - 819 q^{20} - 612 q^{21} - 405 q^{22} - 441 q^{23} - 612 q^{24} - 423 q^{25} - 423 q^{26} - 612 q^{27} - 1299 q^{28} - 423 q^{29} - 612 q^{30} - 423 q^{31} - 369 q^{32} - 612 q^{33} - 369 q^{34} - 387 q^{35} - 684 q^{36} - 1323 q^{37} - 423 q^{38} - 1188 q^{39} - 297 q^{40} - 423 q^{41} - 612 q^{42} - 405 q^{43} - 531 q^{44} - 720 q^{45} - 1503 q^{46} - 585 q^{47} - 864 q^{48} - 549 q^{49} - 837 q^{50} - 792 q^{51} - 855 q^{52} - 675 q^{53} - 828 q^{54} - 1593 q^{55} - 1161 q^{56} - 738 q^{57} - 1107 q^{58} - 729 q^{59} - 1044 q^{60} - 615 q^{61} - 693 q^{62} - 756 q^{63} - 1629 q^{64} - 621 q^{65} - 900 q^{66} - 441 q^{67} - 711 q^{68} - 720 q^{69} - 459 q^{70} - 549 q^{71} - 720 q^{72} - 1233 q^{73} - 423 q^{74} - 612 q^{75} - 396 q^{76} - 693 q^{77} - 612 q^{78} - 255 q^{79} - 423 q^{80} - 612 q^{81} - 1035 q^{82} - 333 q^{83} - 612 q^{84} - 243 q^{85} - 261 q^{86} - 612 q^{87} - 135 q^{88} - 297 q^{89} - 792 q^{90} - 1209 q^{91} - 225 q^{92} - 612 q^{93} - 369 q^{94} - 567 q^{95} - 1476 q^{96} - 621 q^{97} - 909 q^{98} - 864 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3249))\)

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
3249.2.a \(\chi_{3249}(1, \cdot)\) 3249.2.a.a 1 1
3249.2.a.b 1
3249.2.a.c 1
3249.2.a.d 1
3249.2.a.e 1
3249.2.a.f 1
3249.2.a.g 1
3249.2.a.h 2
3249.2.a.i 2
3249.2.a.j 2
3249.2.a.k 2
3249.2.a.l 2
3249.2.a.m 2
3249.2.a.n 2
3249.2.a.o 2
3249.2.a.p 2
3249.2.a.q 2
3249.2.a.r 2
3249.2.a.s 3
3249.2.a.t 3
3249.2.a.u 3
3249.2.a.v 3
3249.2.a.w 3
3249.2.a.x 3
3249.2.a.y 3
3249.2.a.z 3
3249.2.a.ba 4
3249.2.a.bb 4
3249.2.a.bc 4
3249.2.a.bd 4
3249.2.a.be 4
3249.2.a.bf 4
3249.2.a.bg 6
3249.2.a.bh 6
3249.2.a.bi 6
3249.2.a.bj 6
3249.2.a.bk 8
3249.2.a.bl 8
3249.2.a.bm 8
3249.2.a.bn 8
3249.2.d \(\chi_{3249}(3248, \cdot)\) n/a 112 1
3249.2.e \(\chi_{3249}(1084, \cdot)\) n/a 648 2
3249.2.f \(\chi_{3249}(1873, \cdot)\) n/a 266 2
3249.2.g \(\chi_{3249}(292, \cdot)\) n/a 648 2
3249.2.h \(\chi_{3249}(1375, \cdot)\) n/a 648 2
3249.2.k \(\chi_{3249}(2459, \cdot)\) n/a 648 2
3249.2.l \(\chi_{3249}(1082, \cdot)\) n/a 648 2
3249.2.m \(\chi_{3249}(791, \cdot)\) n/a 224 2
3249.2.t \(\chi_{3249}(293, \cdot)\) n/a 648 2
3249.2.u \(\chi_{3249}(28, \cdot)\) n/a 804 6
3249.2.v \(\chi_{3249}(967, \cdot)\) n/a 1944 6
3249.2.w \(\chi_{3249}(1111, \cdot)\) n/a 1944 6
3249.2.x \(\chi_{3249}(488, \cdot)\) n/a 1944 6
3249.2.y \(\chi_{3249}(116, \cdot)\) n/a 684 6
3249.2.bd \(\chi_{3249}(299, \cdot)\) n/a 1944 6
3249.2.bg \(\chi_{3249}(172, \cdot)\) n/a 2844 18
3249.2.bh \(\chi_{3249}(170, \cdot)\) n/a 2304 18
3249.2.bk \(\chi_{3249}(7, \cdot)\) n/a 13608 36
3249.2.bl \(\chi_{3249}(106, \cdot)\) n/a 13608 36
3249.2.bm \(\chi_{3249}(64, \cdot)\) n/a 5688 36
3249.2.bn \(\chi_{3249}(58, \cdot)\) n/a 13608 36
3249.2.bo \(\chi_{3249}(122, \cdot)\) n/a 13608 36
3249.2.bv \(\chi_{3249}(8, \cdot)\) n/a 4608 36
3249.2.bw \(\chi_{3249}(56, \cdot)\) n/a 13608 36
3249.2.bx \(\chi_{3249}(50, \cdot)\) n/a 13608 36
3249.2.ca \(\chi_{3249}(4, \cdot)\) n/a 40824 108
3249.2.cb \(\chi_{3249}(25, \cdot)\) n/a 40824 108
3249.2.cc \(\chi_{3249}(55, \cdot)\) n/a 16956 108
3249.2.cf \(\chi_{3249}(2, \cdot)\) n/a 40824 108
3249.2.ck \(\chi_{3249}(53, \cdot)\) n/a 13608 108
3249.2.cl \(\chi_{3249}(14, \cdot)\) n/a 40824 108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3249))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3249)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 2}\)