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Properties

Label 1045.4.bd
Level $1045$
Weight $4$
Character orbit 1045.bd
Rep. character $\chi_{1045}(12,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1200$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.bd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1456 1200 256
Cusp forms 1424 1200 224
Eisenstein series 32 0 32

Trace form

\( 1200 q + 24 q^{6} + O(q^{10}) \) \( 1200 q + 24 q^{6} - 504 q^{15} + 9528 q^{16} + 96 q^{17} + 576 q^{21} + 384 q^{23} - 636 q^{28} - 2016 q^{32} + 360 q^{35} - 22464 q^{36} - 2844 q^{38} - 288 q^{40} + 720 q^{43} - 1888 q^{45} + 1112 q^{47} - 6132 q^{48} - 4560 q^{51} + 4208 q^{57} - 5472 q^{58} + 6336 q^{60} + 1920 q^{61} - 2000 q^{63} - 3072 q^{68} + 22764 q^{72} - 3648 q^{73} - 7912 q^{76} + 12360 q^{78} + 3668 q^{80} + 50008 q^{81} + 3440 q^{82} - 5584 q^{83} + 15576 q^{86} - 10784 q^{87} - 7260 q^{90} - 13440 q^{91} - 6172 q^{92} - 3696 q^{93} - 6288 q^{95} - 20064 q^{96} - 3168 q^{97} - 8928 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)