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Properties

Label 1176.4.bg
Level $1176$
Weight $4$
Character orbit 1176.bg
Rep. character $\chi_{1176}(169,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $504$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1176.bg (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1176, [\chi])\).

Total New Old
Modular forms 4080 504 3576
Cusp forms 3984 504 3480
Eisenstein series 96 0 96

Trace form

\( 504 q - 6 q^{3} + 24 q^{7} - 756 q^{9} + O(q^{10}) \) \( 504 q - 6 q^{3} + 24 q^{7} - 756 q^{9} + 56 q^{11} + 16 q^{13} + 210 q^{15} + 8 q^{17} + 1412 q^{19} + 30 q^{21} - 168 q^{23} - 2352 q^{25} - 54 q^{27} - 280 q^{29} - 336 q^{31} + 168 q^{33} + 2156 q^{35} - 462 q^{37} - 1050 q^{39} - 888 q^{41} + 196 q^{43} - 380 q^{49} - 1176 q^{53} + 1062 q^{55} - 84 q^{57} + 2084 q^{59} - 1218 q^{61} - 918 q^{63} + 2016 q^{65} + 1764 q^{67} - 48 q^{69} + 3080 q^{73} - 426 q^{75} - 672 q^{77} - 1848 q^{79} - 6804 q^{81} + 9936 q^{83} - 2016 q^{85} + 2370 q^{87} + 1568 q^{89} - 5780 q^{91} + 924 q^{93} - 7280 q^{95} + 120 q^{97} + 504 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1176, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1176, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)