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Properties

Label 1604.2.ba
Level $1604$
Weight $2$
Character orbit 1604.ba
Rep. character $\chi_{1604}(9,\cdot)$
Character field $\Q(\zeta_{200})$
Dimension $2640$
Sturm bound $402$

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Defining parameters

Level: \( N \) \(=\) \( 1604 = 2^{2} \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1604.ba (of order \(200\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 401 \)
Character field: \(\Q(\zeta_{200})\)
Sturm bound: \(402\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1604, [\chi])\).

Total New Old
Modular forms 16320 2640 13680
Cusp forms 15840 2640 13200
Eisenstein series 480 0 480

Trace form

\( 2640 q + O(q^{10}) \) \( 2640 q + 20 q^{11} - 60 q^{19} + 240 q^{21} + 40 q^{25} - 60 q^{27} - 120 q^{29} + 40 q^{33} + 80 q^{39} - 160 q^{41} + 40 q^{43} + 40 q^{49} + 60 q^{55} + 160 q^{61} - 80 q^{63} - 40 q^{71} - 100 q^{75} - 80 q^{77} - 720 q^{81} - 120 q^{83} - 60 q^{89} + 160 q^{93} - 120 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1604, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1604, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1604, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(401, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(802, [\chi])\)\(^{\oplus 2}\)