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Properties

Label 1008.4.s
Level $1008$
Weight $4$
Character orbit 1008.s
Rep. character $\chi_{1008}(289,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $118$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1008, [\chi])\).

Total New Old
Modular forms 1200 122 1078
Cusp forms 1104 118 986
Eisenstein series 96 4 92

Trace form

\( 118 q + q^{5} - 16 q^{7} + O(q^{10}) \) \( 118 q + q^{5} - 16 q^{7} - 11 q^{11} - 4 q^{13} + q^{17} - 23 q^{19} - 41 q^{23} - 1292 q^{25} + 260 q^{29} + 247 q^{31} - 111 q^{35} - 5 q^{37} + 300 q^{41} + 576 q^{43} - 369 q^{47} + 278 q^{49} - 7 q^{53} - 58 q^{55} + 717 q^{59} - 101 q^{61} + 34 q^{65} + 943 q^{67} + 2600 q^{71} + 1091 q^{73} + 223 q^{77} - 851 q^{79} + 304 q^{83} + 1542 q^{85} - 1067 q^{89} - 732 q^{91} + 1149 q^{95} + 2324 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)