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Properties

Label 1150.4.w
Level $1150$
Weight $4$
Character orbit 1150.w
Rep. character $\chi_{1150}(17,\cdot)$
Character field $\Q(\zeta_{220})$
Dimension $14400$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1150.w (of order \(220\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 575 \)
Character field: \(\Q(\zeta_{220})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1150, [\chi])\).

Total New Old
Modular forms 43520 14400 29120
Cusp forms 42880 14400 28480
Eisenstein series 640 0 640

Trace form

\( 14400 q - 16 q^{3} + O(q^{10}) \) \( 14400 q - 16 q^{3} - 64 q^{12} + 192 q^{13} - 5760 q^{16} - 144 q^{18} + 7140 q^{23} - 2000 q^{25} - 1432 q^{27} + 352 q^{28} + 320 q^{29} + 3872 q^{33} - 2752 q^{35} + 12960 q^{36} + 2376 q^{37} + 4880 q^{39} + 13560 q^{47} + 256 q^{48} + 272 q^{50} + 768 q^{52} - 1600 q^{55} + 7656 q^{57} + 9920 q^{59} - 1376 q^{62} + 6160 q^{69} - 9744 q^{70} - 22320 q^{71} + 128 q^{72} + 10224 q^{73} + 17236 q^{75} + 10128 q^{77} - 6400 q^{78} - 31720 q^{81} - 2800 q^{82} - 3060 q^{85} + 2200 q^{87} - 3536 q^{92} + 872 q^{93} + 19048 q^{95} - 25344 q^{97} - 14352 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1150, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1150, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1150, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 2}\)