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Properties

Label 1148.4.cj
Level $1148$
Weight $4$
Character orbit 1148.cj
Rep. character $\chi_{1148}(17,\cdot)$
Character field $\Q(\zeta_{120})$
Dimension $2688$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1148.cj (of order \(120\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{120})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1148, [\chi])\).

Total New Old
Modular forms 16320 2688 13632
Cusp forms 15936 2688 13248
Eisenstein series 384 0 384

Trace form

\( 2688 q + 56 q^{9} + O(q^{10}) \) \( 2688 q + 56 q^{9} + 336 q^{15} + 288 q^{17} + 408 q^{19} - 1168 q^{21} + 512 q^{29} + 1920 q^{33} + 200 q^{35} - 1008 q^{37} + 1856 q^{43} + 1104 q^{47} + 2024 q^{49} + 2520 q^{51} - 928 q^{53} + 5824 q^{57} - 7648 q^{63} + 3056 q^{65} - 528 q^{67} - 3488 q^{71} - 2304 q^{73} + 19824 q^{75} - 720 q^{77} - 1512 q^{79} - 3136 q^{85} + 6024 q^{87} + 4800 q^{89} + 7848 q^{91} - 1568 q^{93} - 4016 q^{95} + 17200 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1148, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1148, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1148, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(574, [\chi])\)\(^{\oplus 2}\)