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Properties

Label 1045.2.cb
Level $1045$
Weight $2$
Character orbit 1045.cb
Rep. character $\chi_{1045}(43,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1392$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.cb (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
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 1488 0
Cusp forms 1392 1392 0
Eisenstein series 96 96 0

Trace form

\( 1392 q - 24 q^{3} - 24 q^{5} + O(q^{10}) \) \( 1392 q - 24 q^{3} - 24 q^{5} - 12 q^{11} - 12 q^{12} - 24 q^{15} - 48 q^{16} - 168 q^{20} - 24 q^{23} - 72 q^{25} + 96 q^{26} - 12 q^{27} - 24 q^{31} - 54 q^{33} - 48 q^{36} - 48 q^{37} + 144 q^{38} - 96 q^{42} - 12 q^{45} - 72 q^{47} - 144 q^{48} + 12 q^{53} - 78 q^{55} - 96 q^{56} + 96 q^{58} + 72 q^{60} - 72 q^{66} + 216 q^{67} - 120 q^{70} - 48 q^{71} - 48 q^{75} - 240 q^{77} - 108 q^{78} + 12 q^{80} - 144 q^{81} + 12 q^{82} - 48 q^{86} - 162 q^{88} + 96 q^{91} - 228 q^{92} + 276 q^{93} - 72 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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