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Properties

Label 1045.2.j
Level $1045$
Weight $2$
Character orbit 1045.j
Rep. character $\chi_{1045}(153,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $216$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 248 216 32
Cusp forms 232 216 16
Eisenstein series 16 0 16

Trace form

\( 216 q + 4 q^{3} + 4 q^{5} + O(q^{10}) \) \( 216 q + 4 q^{3} + 4 q^{5} - 8 q^{11} + 16 q^{12} - 200 q^{16} + 16 q^{20} + 8 q^{22} - 20 q^{23} - 8 q^{25} + 48 q^{26} + 4 q^{27} - 32 q^{31} + 4 q^{33} - 184 q^{36} - 36 q^{37} + 16 q^{42} + 12 q^{45} + 44 q^{47} + 24 q^{48} - 20 q^{55} + 64 q^{58} + 136 q^{60} - 24 q^{66} - 20 q^{67} + 72 q^{71} + 16 q^{75} - 14 q^{77} - 80 q^{78} + 80 q^{80} - 144 q^{81} + 80 q^{86} - 12 q^{88} - 112 q^{91} - 96 q^{92} - 36 q^{93} + 148 q^{97} + O(q^{100}) \)

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.

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

\( S_{2}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)