Properties

Label 3724.2.cw
Level $3724$
Weight $2$
Character orbit 3724.cw
Rep. character $\chi_{3724}(505,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1104$
Sturm bound $1120$

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Defining parameters

Level: \( N \) \(=\) \( 3724 = 2^{2} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3724.cw (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 931 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(1120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3724, [\chi])\).

Total New Old
Modular forms 6792 1104 5688
Cusp forms 6648 1104 5544
Eisenstein series 144 0 144

Trace form

\( 1104 q - 2 q^{5} + 88 q^{9} - 2 q^{11} + 6 q^{13} + 6 q^{15} + 7 q^{17} + 16 q^{19} - 4 q^{21} + 4 q^{23} + 82 q^{25} - 12 q^{27} - 4 q^{29} + 8 q^{33} + 12 q^{35} - 2 q^{37} + 16 q^{39} + 12 q^{41} - 18 q^{43}+ \cdots - 116 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(3724, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3724, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3724, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(931, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1862, [\chi])\)\(^{\oplus 2}\)