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Properties

Label 1045.4.cb
Level $1045$
Weight $4$
Character orbit 1045.cb
Rep. character $\chi_{1045}(43,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $4272$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.cb (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 4368 4368 0
Cusp forms 4272 4272 0
Eisenstein series 96 96 0

Trace form

\( 4272 q - 24 q^{3} - 24 q^{5} + O(q^{10}) \) \( 4272 q - 24 q^{3} - 24 q^{5} - 12 q^{11} - 12 q^{12} - 24 q^{15} - 48 q^{16} + 2232 q^{20} - 492 q^{22} - 24 q^{23} + 408 q^{25} - 744 q^{26} - 12 q^{27} - 24 q^{31} + 1950 q^{33} - 48 q^{36} - 48 q^{37} - 6240 q^{38} - 2616 q^{42} - 12 q^{45} + 2040 q^{47} - 3384 q^{48} - 1896 q^{53} + 5202 q^{55} - 96 q^{56} - 8256 q^{58} - 2328 q^{60} + 216 q^{66} - 3384 q^{67} - 12120 q^{70} - 48 q^{71} - 48 q^{75} + 2076 q^{77} - 108 q^{78} + 6252 q^{80} + 1584 q^{81} + 10308 q^{82} - 48 q^{86} - 3030 q^{88} - 4896 q^{91} - 21180 q^{92} - 5628 q^{93} - 3480 q^{97} + O(q^{100}) \)

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.