↑

Properties

Label 3100.3.eb
Level $3100$
Weight $3$
Character orbit 3100.eb
Rep. character $\chi_{3100}(161,\cdot)$
Character field $\Q(\zeta_{30})$
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.eb (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 1280 q + 12 q^{5} + 8 q^{7} - 460 q^{9} + O(q^{10}) \) \( 1280 q + 12 q^{5} + 8 q^{7} - 460 q^{9} - 90 q^{31} - 40 q^{33} - 6 q^{35} + 72 q^{37} - 45 q^{41} - 468 q^{43} - 146 q^{45} + 42 q^{47} - 4440 q^{49} + 70 q^{51} + 72 q^{53} - 321 q^{55} + 288 q^{57} + 165 q^{59} + 220 q^{63} + 522 q^{65} - 141 q^{67} - 50 q^{69} + 230 q^{71} + 36 q^{73} + 606 q^{75} + 1570 q^{81} + 930 q^{83} + 315 q^{87} - 62 q^{93} - 126 q^{95} + 180 q^{97} + 840 q^{99} + O(q^{100}) \)

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

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