Properties

Label 1140.2.cq
Level $1140$
Weight $2$
Character orbit 1140.cq
Rep. character $\chi_{1140}(17,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $480$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1140.cq (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 285 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1140, [\chi])\).

Total New Old
Modular forms 3024 480 2544
Cusp forms 2736 480 2256
Eisenstein series 288 0 288

Trace form

\( 480q + O(q^{10}) \) \( 480q + 18q^{15} - 24q^{25} + 72q^{33} - 12q^{43} + 18q^{45} + 96q^{51} + 24q^{55} + 18q^{57} + 24q^{61} - 36q^{63} + 48q^{67} + 24q^{85} + 48q^{87} - 72q^{91} + 60q^{93} - 24q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1140, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1140, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)