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Properties

Label 1078.6
Level 1078
Weight 6
Dimension 55485
Nonzero newspaces 16
Sturm bound 423360
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(423360\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(1078))\).

Total New Old
Modular forms 177600 55485 122115
Cusp forms 175200 55485 119715
Eisenstein series 2400 0 2400

Trace form

\( 55485 q + 72 q^{3} - 128 q^{4} + 264 q^{5} + 884 q^{6} + 464 q^{7} - 3772 q^{9} + O(q^{10}) \) \( 55485 q + 72 q^{3} - 128 q^{4} + 264 q^{5} + 884 q^{6} + 464 q^{7} - 3772 q^{9} - 1976 q^{10} + 2 q^{11} + 1312 q^{12} + 13590 q^{13} - 240 q^{14} - 16762 q^{15} - 2048 q^{16} - 13712 q^{17} + 10772 q^{18} + 16307 q^{19} + 9600 q^{20} + 17580 q^{21} + 5664 q^{22} + 9252 q^{23} - 7360 q^{24} - 19512 q^{25} - 62128 q^{26} - 130983 q^{27} - 13312 q^{28} - 19132 q^{29} + 41832 q^{30} + 109814 q^{31} + 5120 q^{32} + 73183 q^{33} + 70768 q^{34} - 21756 q^{35} + 93200 q^{36} - 194564 q^{37} - 49512 q^{38} + 165830 q^{39} + 99200 q^{40} + 261836 q^{41} + 133200 q^{42} + 62666 q^{43} - 11888 q^{44} - 245002 q^{45} - 265280 q^{46} - 261688 q^{47} - 46080 q^{48} - 640540 q^{49} - 52304 q^{50} - 553595 q^{51} - 60032 q^{52} - 179962 q^{53} + 166608 q^{54} + 502684 q^{55} + 253440 q^{56} + 249441 q^{57} + 598016 q^{58} + 363773 q^{59} + 271872 q^{60} - 1365314 q^{61} - 557640 q^{62} - 999708 q^{63} + 163840 q^{64} + 1647172 q^{65} + 2134960 q^{66} + 1533306 q^{67} + 300928 q^{68} + 1750626 q^{69} - 16896 q^{70} - 746160 q^{71} - 341248 q^{72} - 1402672 q^{73} - 866000 q^{74} - 4552265 q^{75} - 528480 q^{76} - 1021452 q^{77} - 1544096 q^{78} - 1748958 q^{79} - 242176 q^{80} - 2471397 q^{81} - 189652 q^{82} + 1489997 q^{83} + 457536 q^{84} + 3622650 q^{85} + 2712404 q^{86} + 8433628 q^{87} + 1002880 q^{88} + 2348132 q^{89} + 2305992 q^{90} + 226528 q^{91} - 157344 q^{92} - 5750254 q^{93} - 2050528 q^{94} - 6686482 q^{95} - 122880 q^{96} - 2023953 q^{97} - 100032 q^{98} + 151258 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(1078))\)

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
1078.6.a \(\chi_{1078}(1, \cdot)\) 1078.6.a.a 1 1
1078.6.a.b 1
1078.6.a.c 1
1078.6.a.d 1
1078.6.a.e 1
1078.6.a.f 1
1078.6.a.g 2
1078.6.a.h 2
1078.6.a.i 2
1078.6.a.j 3
1078.6.a.k 3
1078.6.a.l 4
1078.6.a.m 4
1078.6.a.n 5
1078.6.a.o 6
1078.6.a.p 6
1078.6.a.q 6
1078.6.a.r 8
1078.6.a.s 8
1078.6.a.t 8
1078.6.a.u 8
1078.6.a.v 8
1078.6.a.w 8
1078.6.a.x 8
1078.6.a.y 8
1078.6.a.z 8
1078.6.a.ba 10
1078.6.a.bb 12
1078.6.a.bc 12
1078.6.a.bd 14
1078.6.c \(\chi_{1078}(1077, \cdot)\) n/a 200 1
1078.6.e \(\chi_{1078}(67, \cdot)\) n/a 336 2
1078.6.f \(\chi_{1078}(295, \cdot)\) n/a 820 4
1078.6.i \(\chi_{1078}(901, \cdot)\) n/a 400 2
1078.6.j \(\chi_{1078}(155, \cdot)\) n/a 1416 6
1078.6.l \(\chi_{1078}(195, \cdot)\) n/a 800 4
1078.6.o \(\chi_{1078}(153, \cdot)\) n/a 1680 6
1078.6.q \(\chi_{1078}(361, \cdot)\) n/a 1600 8
1078.6.r \(\chi_{1078}(23, \cdot)\) n/a 2784 12
1078.6.s \(\chi_{1078}(19, \cdot)\) n/a 1600 8
1078.6.v \(\chi_{1078}(15, \cdot)\) n/a 6720 24
1078.6.w \(\chi_{1078}(87, \cdot)\) n/a 3360 12
1078.6.ba \(\chi_{1078}(13, \cdot)\) n/a 6720 24
1078.6.bc \(\chi_{1078}(9, \cdot)\) n/a 13440 48
1078.6.bf \(\chi_{1078}(17, \cdot)\) n/a 13440 48

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(1078))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(1078)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 2}\)