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Properties

Label 1014.4
Level 1014
Weight 4
Dimension 21043
Nonzero newspaces 12
Sturm bound 227136
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(227136\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1014))\).

Total New Old
Modular forms 86088 21043 65045
Cusp forms 84264 21043 63221
Eisenstein series 1824 0 1824

Trace form

\( 21043 q - 2 q^{2} - 3 q^{3} + 4 q^{4} + 6 q^{5} + 6 q^{6} + 272 q^{7} + 88 q^{8} + 9 q^{9} + O(q^{10}) \) \( 21043 q - 2 q^{2} - 3 q^{3} + 4 q^{4} + 6 q^{5} + 6 q^{6} + 272 q^{7} + 88 q^{8} + 9 q^{9} - 372 q^{10} - 468 q^{11} - 108 q^{12} - 576 q^{13} - 448 q^{14} - 306 q^{15} + 16 q^{16} + 822 q^{17} + 198 q^{18} + 2756 q^{19} + 552 q^{20} + 288 q^{21} - 24 q^{22} - 744 q^{23} + 24 q^{24} - 1589 q^{25} - 1683 q^{27} - 64 q^{28} - 750 q^{29} - 1596 q^{30} + 152 q^{31} - 32 q^{32} + 2028 q^{33} + 252 q^{34} + 3024 q^{35} + 1572 q^{36} + 1538 q^{37} - 40 q^{38} + 2244 q^{39} - 48 q^{40} + 750 q^{41} + 1776 q^{42} + 1292 q^{43} + 48 q^{44} - 534 q^{45} - 336 q^{46} - 1584 q^{47} - 48 q^{48} - 807 q^{49} + 1930 q^{50} - 2070 q^{51} + 552 q^{52} + 4374 q^{53} + 3366 q^{54} + 72 q^{55} + 512 q^{56} - 1188 q^{57} - 2436 q^{58} - 5316 q^{59} - 2184 q^{60} - 3190 q^{61} - 8176 q^{62} - 16296 q^{63} - 704 q^{64} - 5358 q^{65} - 5880 q^{66} - 7228 q^{67} - 1128 q^{68} - 7536 q^{69} - 4704 q^{70} - 1320 q^{71} - 456 q^{72} + 4826 q^{73} + 11036 q^{74} + 22707 q^{75} + 11024 q^{76} + 26304 q^{77} + 5832 q^{78} + 21560 q^{79} + 2208 q^{80} + 16305 q^{81} - 636 q^{82} - 5388 q^{83} - 2496 q^{84} - 15168 q^{85} - 6616 q^{86} - 12570 q^{87} - 96 q^{88} - 10950 q^{89} - 4428 q^{90} - 9360 q^{91} - 7776 q^{92} - 19872 q^{93} - 18528 q^{94} - 13320 q^{95} + 96 q^{96} - 28270 q^{97} - 3090 q^{98} - 13572 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1014))\)

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
1014.4.a \(\chi_{1014}(1, \cdot)\) 1014.4.a.a 1 1
1014.4.a.b 1
1014.4.a.c 1
1014.4.a.d 1
1014.4.a.e 1
1014.4.a.f 1
1014.4.a.g 1
1014.4.a.h 1
1014.4.a.i 1
1014.4.a.j 1
1014.4.a.k 1
1014.4.a.l 2
1014.4.a.m 2
1014.4.a.n 2
1014.4.a.o 2
1014.4.a.p 2
1014.4.a.q 2
1014.4.a.r 2
1014.4.a.s 2
1014.4.a.t 3
1014.4.a.u 3
1014.4.a.v 3
1014.4.a.w 3
1014.4.a.x 3
1014.4.a.y 3
1014.4.a.z 4
1014.4.a.ba 4
1014.4.a.bb 6
1014.4.a.bc 6
1014.4.a.bd 6
1014.4.a.be 6
1014.4.b \(\chi_{1014}(337, \cdot)\) 1014.4.b.a 2 1
1014.4.b.b 2
1014.4.b.c 2
1014.4.b.d 2
1014.4.b.e 2
1014.4.b.f 2
1014.4.b.g 2
1014.4.b.h 2
1014.4.b.i 4
1014.4.b.j 4
1014.4.b.k 4
1014.4.b.l 6
1014.4.b.m 6
1014.4.b.n 6
1014.4.b.o 8
1014.4.b.p 12
1014.4.b.q 12
1014.4.e \(\chi_{1014}(529, \cdot)\) n/a 152 2
1014.4.g \(\chi_{1014}(239, \cdot)\) n/a 308 2
1014.4.i \(\chi_{1014}(361, \cdot)\) n/a 156 2
1014.4.k \(\chi_{1014}(89, \cdot)\) n/a 616 4
1014.4.m \(\chi_{1014}(79, \cdot)\) n/a 1104 12
1014.4.p \(\chi_{1014}(25, \cdot)\) n/a 1080 12
1014.4.q \(\chi_{1014}(55, \cdot)\) n/a 2208 24
1014.4.r \(\chi_{1014}(5, \cdot)\) n/a 4368 24
1014.4.u \(\chi_{1014}(43, \cdot)\) n/a 2160 24
1014.4.x \(\chi_{1014}(11, \cdot)\) n/a 8736 48

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1014))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1014)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 2}\)