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Properties

Label 1028.6
Level 1028
Weight 6
Dimension 96062
Nonzero newspaces 9
Sturm bound 396288
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1028 = 2^{2} \cdot 257 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 9 \)
Sturm bound: \(396288\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(1028))\).

Total New Old
Modular forms 165760 96574 69186
Cusp forms 164480 96062 68418
Eisenstein series 1280 512 768

Trace form

\( 96062 q - 128 q^{2} + 24 q^{3} - 128 q^{4} - 364 q^{5} - 128 q^{6} + 176 q^{7} - 128 q^{8} - 58 q^{9} + O(q^{10}) \) \( 96062 q - 128 q^{2} + 24 q^{3} - 128 q^{4} - 364 q^{5} - 128 q^{6} + 176 q^{7} - 128 q^{8} - 58 q^{9} - 128 q^{10} - 1080 q^{11} - 128 q^{12} + 580 q^{13} - 128 q^{14} + 1296 q^{15} - 128 q^{16} - 1444 q^{17} - 128 q^{18} - 1672 q^{19} - 128 q^{20} - 2368 q^{21} - 128 q^{22} + 8208 q^{23} - 128 q^{24} + 162 q^{25} - 128 q^{26} - 8208 q^{27} - 128 q^{28} + 932 q^{29} - 128 q^{30} - 8512 q^{31} - 128 q^{32} + 12704 q^{33} - 128 q^{34} + 9504 q^{35} - 128 q^{36} + 340 q^{37} - 128 q^{38} - 10032 q^{39} - 128 q^{40} - 34708 q^{41} - 128 q^{42} + 24200 q^{43} - 128 q^{44} + 10436 q^{45} - 128 q^{46} + 2592 q^{47} - 128 q^{48} + 17870 q^{49} - 128 q^{50} + 14256 q^{51} - 128 q^{52} - 39244 q^{53} - 128 q^{54} - 58320 q^{55} - 128 q^{56} + 19808 q^{57} - 128 q^{58} + 15336 q^{59} - 128 q^{60} + 69220 q^{61} - 128 q^{62} - 17424 q^{63} - 128 q^{64} + 44888 q^{65} - 128 q^{66} - 43624 q^{67} - 128 q^{68} - 98752 q^{69} - 128 q^{70} + 93744 q^{71} - 128 q^{72} - 135380 q^{73} - 128 q^{74} - 5016 q^{75} - 128 q^{76} + 94784 q^{77} - 128 q^{78} + 153824 q^{79} - 128 q^{80} + 50126 q^{81} - 128 q^{82} - 135432 q^{83} - 128 q^{84} - 64408 q^{85} - 128 q^{86} - 14256 q^{87} - 128 q^{88} - 59764 q^{89} - 128 q^{90} - 73568 q^{91} - 128 q^{92} + 101888 q^{93} - 128 q^{94} - 90288 q^{95} - 128 q^{96} + 244540 q^{97} - 128 q^{98} + 106920 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(1028))\)

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
1028.6.a \(\chi_{1028}(1, \cdot)\) 1028.6.a.a 49 1
1028.6.a.b 57
1028.6.b \(\chi_{1028}(513, \cdot)\) n/a 108 1
1028.6.f \(\chi_{1028}(241, \cdot)\) n/a 216 2
1028.6.g \(\chi_{1028}(193, \cdot)\) n/a 432 4
1028.6.i \(\chi_{1028}(129, \cdot)\) n/a 864 8
1028.6.k \(\chi_{1028}(17, \cdot)\) n/a 1728 16
1028.6.n \(\chi_{1028}(73, \cdot)\) n/a 3456 32
1028.6.p \(\chi_{1028}(9, \cdot)\) n/a 6848 64
1028.6.q \(\chi_{1028}(3, \cdot)\) n/a 82304 128

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(1028))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(1028)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(257))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(514))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(1028))\)\(^{\oplus 1}\)