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Properties

Label 1028.6.f
Level $1028$
Weight $6$
Character orbit 1028.f
Rep. character $\chi_{1028}(241,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $216$
Sturm bound $774$

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Defining parameters

Level: \( N \) \(=\) \( 1028 = 2^{2} \cdot 257 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1028.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 257 \)
Character field: \(\Q(i)\)
Sturm bound: \(774\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1028, [\chi])\).

Total New Old
Modular forms 1296 216 1080
Cusp forms 1284 216 1068
Eisenstein series 12 0 12

Trace form

\( 216 q - 20 q^{3} - 80 q^{5} + O(q^{10}) \) \( 216 q - 20 q^{3} - 80 q^{5} - 484 q^{11} - 1912 q^{15} - 876 q^{17} - 752 q^{19} - 132 q^{23} + 1468 q^{27} - 19422 q^{33} - 856 q^{35} + 9432 q^{37} + 18420 q^{39} + 18610 q^{41} - 24762 q^{43} + 26784 q^{45} - 6204 q^{47} - 36652 q^{51} - 48916 q^{53} - 63158 q^{55} + 35942 q^{63} + 35968 q^{65} - 88260 q^{67} + 63572 q^{69} + 99998 q^{71} + 12428 q^{73} + 126310 q^{75} - 122088 q^{77} - 1615712 q^{81} - 59840 q^{83} - 17296 q^{85} + 183980 q^{87} - 118448 q^{91} - 53566 q^{93} - 456580 q^{95} - 231414 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1028, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(1028, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1028, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(257, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(514, [\chi])\)\(^{\oplus 2}\)