↑

Properties

Label 1716.2.cq
Level $1716$
Weight $2$
Character orbit 1716.cq
Rep. character $\chi_{1716}(5,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $448$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1716.cq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 429 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1716, [\chi])\).

Total New Old
Modular forms 2784 448 2336
Cusp forms 2592 448 2144
Eisenstein series 192 0 192

Trace form

\( 448 q + O(q^{10}) \) \( 448 q - 8 q^{13} - 12 q^{15} + 8 q^{19} + 24 q^{21} - 24 q^{27} + 16 q^{31} - 38 q^{33} - 24 q^{39} - 4 q^{45} + 24 q^{55} - 12 q^{57} - 24 q^{61} + 28 q^{63} + 48 q^{67} + 32 q^{79} + 8 q^{81} - 40 q^{85} - 96 q^{87} - 32 q^{91} + 38 q^{93} + 64 q^{97} + 100 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1716, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1716, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1716, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(429, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(858, [\chi])\)\(^{\oplus 2}\)