↑

Properties

Label 2100.2.w
Level $2100$
Weight $2$
Character orbit 2100.w
Rep. character $\chi_{2100}(1007,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $560$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 420 \)
Character field: \(\Q(i)\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2100, [\chi])\).

Total New Old
Modular forms 1008 592 416
Cusp forms 912 560 352
Eisenstein series 96 32 64

Trace form

\( 560 q + O(q^{10}) \) \( 560 q - 16 q^{16} + 12 q^{18} + 8 q^{21} + 24 q^{22} + 36 q^{28} + 24 q^{36} + 16 q^{37} + 16 q^{42} - 16 q^{46} + 32 q^{58} + 16 q^{72} - 116 q^{78} + 144 q^{81} + 96 q^{88} + 32 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \)