Properties

Label 1045.2.cc
Level $1045$
Weight $2$
Character orbit 1045.cc
Rep. character $\chi_{1045}(67,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1200$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.cc (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1045, [\chi])\).

Total New Old
Modular forms 1488 1200 288
Cusp forms 1392 1200 192
Eisenstein series 96 0 96

Trace form

\( 1200 q - 24 q^{6} + O(q^{10}) \) \( 1200 q - 24 q^{6} - 36 q^{15} - 72 q^{16} + 36 q^{17} - 96 q^{21} - 24 q^{23} - 72 q^{28} - 72 q^{32} + 36 q^{35} - 96 q^{36} + 36 q^{38} - 72 q^{40} - 96 q^{43} - 36 q^{45} + 72 q^{47} - 168 q^{48} + 60 q^{57} - 144 q^{58} - 288 q^{60} + 48 q^{61} + 144 q^{63} - 180 q^{65} - 192 q^{72} - 96 q^{76} + 264 q^{78} + 252 q^{80} + 96 q^{81} - 300 q^{82} + 312 q^{86} + 420 q^{90} + 144 q^{91} + 276 q^{92} - 144 q^{93} + 72 q^{95} + 96 q^{96} + 72 q^{97} - 144 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

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