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Properties

Label 1176.4.bw
Level $1176$
Weight $4$
Character orbit 1176.bw
Rep. character $\chi_{1176}(25,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1008$
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.bw (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 8160 1008 7152
Cusp forms 7968 1008 6960
Eisenstein series 192 0 192

Trace form

\( 1008 q + 6 q^{3} - 24 q^{7} + 756 q^{9} + O(q^{10}) \) \( 1008 q + 6 q^{3} - 24 q^{7} + 756 q^{9} + 28 q^{11} + 140 q^{13} - 210 q^{15} + 4 q^{17} - 1346 q^{19} + 60 q^{21} - 84 q^{23} + 1974 q^{25} - 108 q^{27} + 280 q^{29} - 168 q^{31} - 114 q^{33} - 1112 q^{35} + 1092 q^{37} + 1680 q^{39} + 888 q^{41} - 196 q^{43} - 268 q^{49} - 588 q^{53} - 2754 q^{55} + 84 q^{57} - 3068 q^{59} + 318 q^{61} + 1080 q^{63} + 1008 q^{65} + 882 q^{67} + 1704 q^{69} - 1550 q^{73} + 1362 q^{75} + 1140 q^{77} - 924 q^{79} + 6804 q^{81} + 3624 q^{83} + 2016 q^{85} - 3792 q^{87} - 5168 q^{89} - 3274 q^{91} + 462 q^{93} - 18928 q^{95} - 12900 q^{97} - 504 q^{99} + O(q^{100}) \)

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

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