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Properties

Label 1001.2.p
Level $1001$
Weight $2$
Character orbit 1001.p
Rep. character $\chi_{1001}(736,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $168$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1001.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(i)\)
Sturm bound: \(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1001, [\chi])\).

Total New Old
Modular forms 232 168 64
Cusp forms 216 168 48
Eisenstein series 16 0 16

Trace form

\( 168 q + 168 q^{9} + O(q^{10}) \) \( 168 q + 168 q^{9} - 24 q^{15} - 200 q^{16} - 40 q^{20} - 24 q^{22} - 56 q^{26} - 48 q^{27} + 48 q^{31} + 4 q^{33} - 8 q^{34} + 52 q^{44} + 48 q^{45} - 48 q^{47} + 64 q^{48} + 48 q^{53} + 96 q^{55} - 80 q^{58} + 8 q^{59} - 72 q^{60} - 88 q^{66} - 56 q^{67} - 24 q^{70} - 56 q^{71} + 184 q^{78} + 144 q^{80} + 56 q^{81} + 96 q^{86} + 16 q^{89} + 64 q^{92} + 8 q^{93} - 64 q^{97} - 132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1001, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1001, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)