↑

Properties

Label 3100.3.dk
Level $3100$
Weight $3$
Character orbit 3100.dk
Rep. character $\chi_{3100}(97,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1280$
Sturm bound $1440$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3100.dk (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3100, [\chi])\).

Total New Old
Modular forms 7728 1280 6448
Cusp forms 7632 1280 6352
Eisenstein series 96 0 96

Trace form

\( 1280 q - 4 q^{3} + 16 q^{7} - 50 q^{9} + O(q^{10}) \) \( 1280 q - 4 q^{3} + 16 q^{7} - 50 q^{9} - 96 q^{15} + 28 q^{23} + 76 q^{25} - 70 q^{27} - 212 q^{33} - 162 q^{35} - 266 q^{37} + 168 q^{43} + 182 q^{45} + 234 q^{47} - 40 q^{53} - 50 q^{55} - 428 q^{57} - 316 q^{63} + 474 q^{65} - 186 q^{67} - 750 q^{69} + 180 q^{71} + 192 q^{73} + 428 q^{75} - 148 q^{77} + 200 q^{79} + 2810 q^{81} - 314 q^{83} + 624 q^{85} + 448 q^{87} - 150 q^{89} - 92 q^{93} - 936 q^{95} + 352 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(3100, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(3100, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(3100, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1550, [\chi])\)\(^{\oplus 2}\)