Properties

Label 2100.4.bu
Level $2100$
Weight $4$
Character orbit 2100.bu
Rep. character $\chi_{2100}(169,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $368$
Sturm bound $1920$

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Defining parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2100.bu (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2100, [\chi])\).

Total New Old
Modular forms 5808 368 5440
Cusp forms 5712 368 5344
Eisenstein series 96 0 96

Trace form

\( 368 q - 24 q^{5} + 828 q^{9} + 24 q^{15} - 72 q^{19} - 84 q^{21} + 440 q^{23} + 540 q^{25} - 496 q^{29} - 960 q^{33} - 56 q^{35} + 1400 q^{37} - 224 q^{41} + 216 q^{45} - 3440 q^{47} - 18032 q^{49} + 1632 q^{51}+ \cdots - 5280 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2100, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)