Properties

Label 3015.2
Level 3015
Weight 2
Dimension 232638
Nonzero newspaces 60
Sturm bound 1292544
Trace bound 6

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Defining parameters

Level: \( N \) = \( 3015 = 3^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 60 \)
Sturm bound: \(1292544\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3015))\).

Total New Old
Modular forms 327360 236150 91210
Cusp forms 318913 232638 86275
Eisenstein series 8447 3512 4935

Trace form

\( 232638 q - 184 q^{2} - 248 q^{3} - 176 q^{4} - 279 q^{5} - 760 q^{6} - 174 q^{7} - 192 q^{8} - 256 q^{9} + O(q^{10}) \) \( 232638 q - 184 q^{2} - 248 q^{3} - 176 q^{4} - 279 q^{5} - 760 q^{6} - 174 q^{7} - 192 q^{8} - 256 q^{9} - 861 q^{10} - 586 q^{11} - 280 q^{12} - 194 q^{13} - 222 q^{14} - 404 q^{15} - 580 q^{16} - 202 q^{17} - 296 q^{18} - 554 q^{19} - 347 q^{20} - 792 q^{21} - 214 q^{22} - 222 q^{23} - 336 q^{24} - 303 q^{25} - 622 q^{26} - 296 q^{27} - 610 q^{28} - 242 q^{29} - 460 q^{30} - 578 q^{31} - 224 q^{32} - 280 q^{33} - 226 q^{34} - 281 q^{35} - 728 q^{36} - 598 q^{37} - 166 q^{38} - 200 q^{39} - 251 q^{40} - 494 q^{41} - 192 q^{42} - 134 q^{43} - 62 q^{44} - 340 q^{45} - 1702 q^{46} - 118 q^{47} - 184 q^{48} - 204 q^{49} - 235 q^{50} - 760 q^{51} - 114 q^{52} - 136 q^{53} - 256 q^{54} - 816 q^{55} - 246 q^{56} - 296 q^{57} + 14 q^{58} - 154 q^{59} - 436 q^{60} - 382 q^{61} - 234 q^{62} - 384 q^{63} - 32 q^{64} - 289 q^{65} - 968 q^{66} - 90 q^{67} - 272 q^{68} - 384 q^{69} - 153 q^{70} - 458 q^{71} - 312 q^{72} - 304 q^{73} - 62 q^{74} - 380 q^{75} - 138 q^{76} - 42 q^{77} - 184 q^{78} - 20 q^{79} - 29 q^{80} - 712 q^{81} - 336 q^{82} + 12 q^{83} - 120 q^{84} - 285 q^{85} - 394 q^{86} - 176 q^{87} - 198 q^{88} - 66 q^{89} - 188 q^{90} - 1686 q^{91} - 6 q^{92} - 144 q^{93} - 190 q^{94} - 217 q^{95} - 680 q^{96} - 202 q^{97} - 32 q^{98} - 224 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3015))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3015.2.a \(\chi_{3015}(1, \cdot)\) 3015.2.a.a 1 1
3015.2.a.b 1
3015.2.a.c 1
3015.2.a.d 2
3015.2.a.e 2
3015.2.a.f 4
3015.2.a.g 4
3015.2.a.h 4
3015.2.a.i 4
3015.2.a.j 5
3015.2.a.k 5
3015.2.a.l 7
3015.2.a.m 7
3015.2.a.n 8
3015.2.a.o 9
3015.2.a.p 9
3015.2.a.q 11
3015.2.a.r 13
3015.2.a.s 13
3015.2.c \(\chi_{3015}(604, \cdot)\) n/a 164 1
3015.2.e \(\chi_{3015}(3014, \cdot)\) n/a 136 1
3015.2.g \(\chi_{3015}(2411, \cdot)\) 3015.2.g.a 4 1
3015.2.g.b 4
3015.2.g.c 40
3015.2.g.d 40
3015.2.i \(\chi_{3015}(1006, \cdot)\) n/a 528 2
3015.2.j \(\chi_{3015}(766, \cdot)\) n/a 228 2
3015.2.k \(\chi_{3015}(841, \cdot)\) n/a 544 2
3015.2.l \(\chi_{3015}(2776, \cdot)\) n/a 544 2
3015.2.m \(\chi_{3015}(937, \cdot)\) n/a 336 2
3015.2.n \(\chi_{3015}(872, \cdot)\) n/a 264 2
3015.2.q \(\chi_{3015}(164, \cdot)\) n/a 808 2
3015.2.s \(\chi_{3015}(364, \cdot)\) n/a 808 2
3015.2.v \(\chi_{3015}(641, \cdot)\) n/a 544 2
3015.2.y \(\chi_{3015}(566, \cdot)\) n/a 184 2
3015.2.z \(\chi_{3015}(401, \cdot)\) n/a 544 2
3015.2.be \(\chi_{3015}(1444, \cdot)\) n/a 808 2
3015.2.bf \(\chi_{3015}(1169, \cdot)\) n/a 272 2
3015.2.bg \(\chi_{3015}(1004, \cdot)\) n/a 808 2
3015.2.bj \(\chi_{3015}(1609, \cdot)\) n/a 792 2
3015.2.bk \(\chi_{3015}(1369, \cdot)\) n/a 336 2
3015.2.bo \(\chi_{3015}(1244, \cdot)\) n/a 808 2
3015.2.bq \(\chi_{3015}(2576, \cdot)\) n/a 544 2
3015.2.bs \(\chi_{3015}(91, \cdot)\) n/a 1120 10
3015.2.bv \(\chi_{3015}(833, \cdot)\) n/a 1616 4
3015.2.bw \(\chi_{3015}(97, \cdot)\) n/a 1616 4
3015.2.bx \(\chi_{3015}(632, \cdot)\) n/a 1616 4
3015.2.by \(\chi_{3015}(1102, \cdot)\) n/a 1616 4
3015.2.cd \(\chi_{3015}(172, \cdot)\) n/a 672 4
3015.2.ce \(\chi_{3015}(68, \cdot)\) n/a 1584 4
3015.2.cf \(\chi_{3015}(133, \cdot)\) n/a 1616 4
3015.2.cg \(\chi_{3015}(908, \cdot)\) n/a 544 4
3015.2.ck \(\chi_{3015}(161, \cdot)\) n/a 880 10
3015.2.cm \(\chi_{3015}(179, \cdot)\) n/a 1360 10
3015.2.co \(\chi_{3015}(64, \cdot)\) n/a 1680 10
3015.2.cq \(\chi_{3015}(16, \cdot)\) n/a 5440 20
3015.2.cr \(\chi_{3015}(121, \cdot)\) n/a 5440 20
3015.2.cs \(\chi_{3015}(181, \cdot)\) n/a 2280 20
3015.2.ct \(\chi_{3015}(76, \cdot)\) n/a 5440 20
3015.2.cw \(\chi_{3015}(62, \cdot)\) n/a 2720 20
3015.2.cx \(\chi_{3015}(253, \cdot)\) n/a 3360 20
3015.2.cz \(\chi_{3015}(41, \cdot)\) n/a 5440 20
3015.2.db \(\chi_{3015}(74, \cdot)\) n/a 8080 20
3015.2.df \(\chi_{3015}(19, \cdot)\) n/a 3360 20
3015.2.dg \(\chi_{3015}(349, \cdot)\) n/a 8080 20
3015.2.dj \(\chi_{3015}(119, \cdot)\) n/a 8080 20
3015.2.dk \(\chi_{3015}(44, \cdot)\) n/a 2720 20
3015.2.dl \(\chi_{3015}(49, \cdot)\) n/a 8080 20
3015.2.dq \(\chi_{3015}(176, \cdot)\) n/a 5440 20
3015.2.dr \(\chi_{3015}(251, \cdot)\) n/a 1840 20
3015.2.du \(\chi_{3015}(11, \cdot)\) n/a 5440 20
3015.2.dx \(\chi_{3015}(4, \cdot)\) n/a 8080 20
3015.2.dz \(\chi_{3015}(599, \cdot)\) n/a 8080 20
3015.2.ec \(\chi_{3015}(17, \cdot)\) n/a 5440 40
3015.2.ed \(\chi_{3015}(43, \cdot)\) n/a 16160 40
3015.2.ee \(\chi_{3015}(92, \cdot)\) n/a 16160 40
3015.2.ef \(\chi_{3015}(28, \cdot)\) n/a 6720 40
3015.2.ek \(\chi_{3015}(7, \cdot)\) n/a 16160 40
3015.2.el \(\chi_{3015}(23, \cdot)\) n/a 16160 40
3015.2.em \(\chi_{3015}(178, \cdot)\) n/a 16160 40
3015.2.en \(\chi_{3015}(83, \cdot)\) n/a 16160 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3015))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3015)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(201))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(335))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(603))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1005))\)\(^{\oplus 2}\)