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Properties

Label 1045.4.cm
Level $1045$
Weight $4$
Character orbit 1045.cm
Rep. character $\chi_{1045}(41,\cdot)$
Character field $\Q(\zeta_{90})$
Dimension $5760$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.cm (of order \(90\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{90})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1045, [\chi])\).

Total New Old
Modular forms 8736 5760 2976
Cusp forms 8544 5760 2784
Eisenstein series 192 0 192

Trace form

\( 5760 q + 12 q^{3} - 300 q^{6} - 180 q^{9} + O(q^{10}) \) \( 5760 q + 12 q^{3} - 300 q^{6} - 180 q^{9} - 72 q^{14} - 60 q^{17} + 384 q^{22} + 3600 q^{24} + 360 q^{26} - 2628 q^{27} - 6000 q^{29} + 180 q^{31} - 4680 q^{33} - 120 q^{34} + 6720 q^{36} - 1584 q^{38} - 3330 q^{41} - 10014 q^{42} - 11286 q^{44} - 3720 q^{47} + 10986 q^{48} - 37560 q^{49} - 8700 q^{51} - 4350 q^{52} + 3528 q^{53} + 5184 q^{58} - 6414 q^{59} - 8040 q^{62} + 46080 q^{64} - 60 q^{66} - 4644 q^{67} - 10800 q^{69} + 9720 q^{70} - 1500 q^{71} - 10944 q^{77} + 38400 q^{78} + 23424 q^{81} + 9396 q^{82} + 2040 q^{86} + 11664 q^{88} - 21384 q^{89} - 5094 q^{91} - 4032 q^{93} + 44160 q^{96} - 9738 q^{97} + 10632 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)