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Properties

Label 1176.2.bg
Level $1176$
Weight $2$
Character orbit 1176.bg
Rep. character $\chi_{1176}(169,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $168$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1176.bg (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1176, [\chi])\).

Total New Old
Modular forms 1392 168 1224
Cusp forms 1296 168 1128
Eisenstein series 96 0 96

Trace form

\( 168 q + 2 q^{3} - 28 q^{9} + O(q^{10}) \) \( 168 q + 2 q^{3} - 28 q^{9} - 8 q^{11} + 10 q^{15} - 8 q^{17} - 76 q^{19} + 2 q^{21} + 24 q^{23} - 16 q^{25} + 2 q^{27} - 8 q^{29} + 8 q^{33} + 28 q^{35} - 18 q^{37} - 10 q^{39} + 24 q^{41} - 12 q^{43} + 12 q^{49} + 24 q^{53} + 30 q^{55} + 4 q^{57} + 4 q^{59} + 2 q^{61} - 14 q^{63} - 12 q^{67} - 16 q^{69} - 8 q^{73} - 2 q^{75} + 24 q^{79} - 28 q^{81} + 48 q^{83} + 64 q^{85} + 10 q^{87} + 64 q^{89} + 76 q^{91} + 4 q^{93} + 80 q^{95} + 200 q^{97} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1176, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces

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