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Properties

Label 1014.6
Level 1014
Weight 6
Dimension 35071
Nonzero newspaces 12
Sturm bound 340704
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(340704\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(1014))\).

Total New Old
Modular forms 142872 35071 107801
Cusp forms 141048 35071 105977
Eisenstein series 1824 0 1824

Trace form

\( 35071 q + 4 q^{2} - 9 q^{3} + 16 q^{4} - 66 q^{5} - 36 q^{6} + 2560 q^{7} - 704 q^{8} - 567 q^{9} + O(q^{10}) \) \( 35071 q + 4 q^{2} - 9 q^{3} + 16 q^{4} - 66 q^{5} - 36 q^{6} + 2560 q^{7} - 704 q^{8} - 567 q^{9} - 504 q^{10} + 4212 q^{11} + 1008 q^{12} + 6288 q^{13} + 2816 q^{14} - 4158 q^{15} - 3840 q^{16} - 4290 q^{17} - 3564 q^{18} - 19988 q^{19} + 6816 q^{20} - 1320 q^{21} - 240 q^{22} + 13512 q^{23} - 576 q^{24} + 38731 q^{25} + 29583 q^{27} + 2816 q^{28} - 12126 q^{29} + 39048 q^{30} - 55960 q^{31} + 1024 q^{32} + 84 q^{33} - 1656 q^{34} + 23184 q^{35} - 40944 q^{36} + 64994 q^{37} + 3824 q^{38} - 45804 q^{39} - 4224 q^{40} + 11766 q^{41} - 6624 q^{42} - 134588 q^{43} - 960 q^{44} + 238866 q^{45} + 2400 q^{46} - 9648 q^{47} - 2304 q^{48} + 43433 q^{49} + 143116 q^{50} + 128574 q^{51} + 5856 q^{52} - 97938 q^{53} - 239364 q^{54} - 478680 q^{55} - 157696 q^{56} - 348972 q^{57} - 150936 q^{58} - 199644 q^{59} + 56352 q^{60} - 98950 q^{61} + 434336 q^{62} + 373008 q^{63} + 53248 q^{64} + 413502 q^{65} + 345840 q^{66} + 810412 q^{67} + 12768 q^{68} + 346200 q^{69} - 242880 q^{70} - 281400 q^{71} - 212928 q^{72} - 458870 q^{73} - 79384 q^{74} - 1100079 q^{75} - 319808 q^{76} - 1320672 q^{77} - 214128 q^{78} - 1082296 q^{79} + 109056 q^{80} + 625929 q^{81} - 484680 q^{82} - 425652 q^{83} - 65664 q^{84} + 807096 q^{85} + 391568 q^{86} + 1532154 q^{87} - 3840 q^{88} + 1149258 q^{89} + 367416 q^{90} + 832936 q^{91} + 717696 q^{92} + 36264 q^{93} + 1020480 q^{94} + 421704 q^{95} - 9216 q^{96} - 2192830 q^{97} - 434460 q^{98} - 544068 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(1014))\)

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
1014.6.a \(\chi_{1014}(1, \cdot)\) 1014.6.a.a 1 1
1014.6.a.b 1
1014.6.a.c 1
1014.6.a.d 1
1014.6.a.e 1
1014.6.a.f 1
1014.6.a.g 1
1014.6.a.h 2
1014.6.a.i 2
1014.6.a.j 2
1014.6.a.k 2
1014.6.a.l 2
1014.6.a.m 2
1014.6.a.n 3
1014.6.a.o 3
1014.6.a.p 3
1014.6.a.q 3
1014.6.a.r 3
1014.6.a.s 3
1014.6.a.t 4
1014.6.a.u 4
1014.6.a.v 6
1014.6.a.w 6
1014.6.a.x 6
1014.6.a.y 6
1014.6.a.z 6
1014.6.a.ba 6
1014.6.a.bb 6
1014.6.a.bc 6
1014.6.a.bd 9
1014.6.a.be 9
1014.6.a.bf 9
1014.6.a.bg 9
1014.6.b \(\chi_{1014}(337, \cdot)\) n/a 126 1
1014.6.e \(\chi_{1014}(529, \cdot)\) n/a 260 2
1014.6.g \(\chi_{1014}(239, \cdot)\) n/a 516 2
1014.6.i \(\chi_{1014}(361, \cdot)\) n/a 256 2
1014.6.k \(\chi_{1014}(89, \cdot)\) n/a 1024 4
1014.6.m \(\chi_{1014}(79, \cdot)\) n/a 1824 12
1014.6.p \(\chi_{1014}(25, \cdot)\) n/a 1848 12
1014.6.q \(\chi_{1014}(55, \cdot)\) n/a 3600 24
1014.6.r \(\chi_{1014}(5, \cdot)\) n/a 7248 24
1014.6.u \(\chi_{1014}(43, \cdot)\) n/a 3648 24
1014.6.x \(\chi_{1014}(11, \cdot)\) n/a 14592 48

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(1014))\) into lower level spaces

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