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Properties

Label 1176.4.ci
Level $1176$
Weight $4$
Character orbit 1176.ci
Rep. character $\chi_{1176}(17,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2016$
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.ci (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 8160 2016 6144
Cusp forms 7968 2016 5952
Eisenstein series 192 0 192

Trace form

\( 2016 q - 12 q^{7} - 112 q^{9} + O(q^{10}) \) \( 2016 q - 12 q^{7} - 112 q^{9} + 270 q^{19} - 50 q^{21} + 4074 q^{25} - 216 q^{31} + 372 q^{33} + 924 q^{37} - 210 q^{39} - 588 q^{43} + 1918 q^{45} - 60 q^{49} + 294 q^{51} - 4998 q^{55} - 112 q^{57} + 1782 q^{61} - 1096 q^{63} + 126 q^{67} + 5460 q^{69} + 1206 q^{73} - 5874 q^{75} + 588 q^{79} + 12796 q^{81} + 840 q^{85} + 4978 q^{87} - 9978 q^{91} - 12096 q^{93} - 1260 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1176, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)