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Properties

Label 3078.2
Level 3078
Weight 2
Dimension 68736
Nonzero newspaces 52
Sturm bound 1049760
Trace bound 43

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Defining parameters

Level: \( N \) = \( 3078 = 2 \cdot 3^{4} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 52 \)
Sturm bound: \(1049760\)
Trace bound: \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3078))\).

Total New Old
Modular forms 266328 68736 197592
Cusp forms 258553 68736 189817
Eisenstein series 7775 0 7775

Trace form

\( 68736 q - 12 q^{5} - 12 q^{7} - 6 q^{8} + O(q^{10}) \) \( 68736 q - 12 q^{5} - 12 q^{7} - 6 q^{8} - 12 q^{10} - 30 q^{11} - 24 q^{13} - 12 q^{14} - 24 q^{17} + 18 q^{18} + 18 q^{19} + 60 q^{20} + 108 q^{21} + 42 q^{22} + 156 q^{23} + 72 q^{25} + 180 q^{26} + 108 q^{27} + 48 q^{28} + 168 q^{29} + 108 q^{30} + 72 q^{31} + 108 q^{33} + 30 q^{34} + 120 q^{35} + 36 q^{36} + 12 q^{37} - 3 q^{38} - 12 q^{40} + 6 q^{41} - 18 q^{43} - 12 q^{44} + 108 q^{45} - 24 q^{46} + 108 q^{47} + 24 q^{49} - 72 q^{50} + 126 q^{51} - 24 q^{52} + 60 q^{53} + 72 q^{55} - 12 q^{56} + 54 q^{57} - 48 q^{58} + 138 q^{59} + 36 q^{61} - 48 q^{62} + 108 q^{63} - 6 q^{64} - 24 q^{65} - 144 q^{66} + 90 q^{67} - 60 q^{68} - 252 q^{69} + 48 q^{70} - 240 q^{71} - 144 q^{72} - 84 q^{73} - 228 q^{74} - 360 q^{75} + 15 q^{76} - 492 q^{77} - 288 q^{78} + 120 q^{79} - 48 q^{80} - 288 q^{81} - 12 q^{82} - 288 q^{83} - 72 q^{84} + 72 q^{85} - 234 q^{86} - 576 q^{87} + 42 q^{88} - 348 q^{89} - 288 q^{90} - 60 q^{91} - 132 q^{92} - 252 q^{93} + 36 q^{94} - 84 q^{95} - 36 q^{96} + 30 q^{97} - 174 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3078))\)

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
3078.2.a \(\chi_{3078}(1, \cdot)\) 3078.2.a.a 1 1
3078.2.a.b 1
3078.2.a.c 1
3078.2.a.d 1
3078.2.a.e 1
3078.2.a.f 1
3078.2.a.g 2
3078.2.a.h 2
3078.2.a.i 2
3078.2.a.j 2
3078.2.a.k 3
3078.2.a.l 3
3078.2.a.m 3
3078.2.a.n 3
3078.2.a.o 3
3078.2.a.p 3
3078.2.a.q 4
3078.2.a.r 4
3078.2.a.s 4
3078.2.a.t 4
3078.2.a.u 6
3078.2.a.v 6
3078.2.a.w 6
3078.2.a.x 6
3078.2.b \(\chi_{3078}(3077, \cdot)\) 3078.2.b.a 20 1
3078.2.b.b 20
3078.2.b.c 20
3078.2.b.d 20
3078.2.e \(\chi_{3078}(1027, \cdot)\) n/a 144 2
3078.2.f \(\chi_{3078}(2215, \cdot)\) n/a 160 2
3078.2.g \(\chi_{3078}(163, \cdot)\) n/a 160 2
3078.2.h \(\chi_{3078}(919, \cdot)\) n/a 160 2
3078.2.j \(\chi_{3078}(1889, \cdot)\) n/a 160 2
3078.2.n \(\chi_{3078}(107, \cdot)\) n/a 160 2
3078.2.p \(\chi_{3078}(1025, \cdot)\) n/a 160 2
3078.2.s \(\chi_{3078}(1133, \cdot)\) n/a 160 2
3078.2.u \(\chi_{3078}(73, \cdot)\) n/a 360 6
3078.2.v \(\chi_{3078}(397, \cdot)\) n/a 360 6
3078.2.w \(\chi_{3078}(973, \cdot)\) n/a 480 6
3078.2.x \(\chi_{3078}(271, \cdot)\) n/a 480 6
3078.2.y \(\chi_{3078}(289, \cdot)\) n/a 360 6
3078.2.z \(\chi_{3078}(739, \cdot)\) n/a 360 6
3078.2.ba \(\chi_{3078}(343, \cdot)\) n/a 324 6
3078.2.bb \(\chi_{3078}(235, \cdot)\) n/a 360 6
3078.2.bc \(\chi_{3078}(505, \cdot)\) n/a 360 6
3078.2.bd \(\chi_{3078}(1441, \cdot)\) n/a 360 6
3078.2.be \(\chi_{3078}(55, \cdot)\) n/a 480 6
3078.2.bf \(\chi_{3078}(199, \cdot)\) n/a 360 6
3078.2.bg \(\chi_{3078}(395, \cdot)\) n/a 360 6
3078.2.bk \(\chi_{3078}(431, \cdot)\) n/a 480 6
3078.2.bo \(\chi_{3078}(485, \cdot)\) n/a 480 6
3078.2.br \(\chi_{3078}(71, \cdot)\) n/a 360 6
3078.2.bv \(\chi_{3078}(449, \cdot)\) n/a 360 6
3078.2.bz \(\chi_{3078}(179, \cdot)\) n/a 360 6
3078.2.cb \(\chi_{3078}(341, \cdot)\) n/a 360 6
3078.2.cd \(\chi_{3078}(611, \cdot)\) n/a 360 6
3078.2.cf \(\chi_{3078}(89, \cdot)\) n/a 360 6
3078.2.ck \(\chi_{3078}(53, \cdot)\) n/a 480 6
3078.2.cm \(\chi_{3078}(629, \cdot)\) n/a 360 6
3078.2.co \(\chi_{3078}(773, \cdot)\) n/a 360 6
3078.2.cq \(\chi_{3078}(385, \cdot)\) n/a 3240 18
3078.2.cr \(\chi_{3078}(43, \cdot)\) n/a 3240 18
3078.2.cs \(\chi_{3078}(25, \cdot)\) n/a 3240 18
3078.2.ct \(\chi_{3078}(301, \cdot)\) n/a 3240 18
3078.2.cu \(\chi_{3078}(115, \cdot)\) n/a 2916 18
3078.2.cv \(\chi_{3078}(121, \cdot)\) n/a 3240 18
3078.2.cw \(\chi_{3078}(7, \cdot)\) n/a 3240 18
3078.2.cx \(\chi_{3078}(61, \cdot)\) n/a 3240 18
3078.2.cy \(\chi_{3078}(139, \cdot)\) n/a 3240 18
3078.2.cz \(\chi_{3078}(155, \cdot)\) n/a 3240 18
3078.2.de \(\chi_{3078}(29, \cdot)\) n/a 3240 18
3078.2.dj \(\chi_{3078}(65, \cdot)\) n/a 3240 18
3078.2.dk \(\chi_{3078}(113, \cdot)\) n/a 3240 18
3078.2.dp \(\chi_{3078}(293, \cdot)\) n/a 3240 18
3078.2.dq \(\chi_{3078}(41, \cdot)\) n/a 3240 18
3078.2.dt \(\chi_{3078}(59, \cdot)\) n/a 3240 18
3078.2.dw \(\chi_{3078}(257, \cdot)\) n/a 3240 18
3078.2.dy \(\chi_{3078}(167, \cdot)\) n/a 3240 18

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3078))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3078)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(513))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1026))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1539))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3078))\)\(^{\oplus 1}\)