↑

Properties

Label 3100.3.bz
Level $3100$
Weight $3$
Character orbit 3100.bz
Rep. character $\chi_{3100}(581,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $640$
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.bz (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 3864 640 3224
Cusp forms 3816 640 3176
Eisenstein series 48 0 48

Trace form

\( 640 q + 5 q^{3} - 6 q^{5} + 16 q^{7} + 485 q^{9} + O(q^{10}) \) \( 640 q + 5 q^{3} - 6 q^{5} + 16 q^{7} + 485 q^{9} + 75 q^{15} + 10 q^{23} - 42 q^{25} + 125 q^{27} - 10 q^{31} - 97 q^{33} - 93 q^{35} - 205 q^{37} - 15 q^{41} + 90 q^{43} + 43 q^{45} - 127 q^{47} - 1040 q^{49} + 265 q^{51} - 110 q^{53} - 205 q^{55} + 180 q^{59} + 20 q^{63} + 115 q^{65} - 87 q^{67} - 150 q^{69} - 130 q^{71} - 300 q^{73} + 100 q^{75} - 380 q^{77} - 100 q^{79} - 1520 q^{81} - 265 q^{83} - 460 q^{85} + 54 q^{87} + 75 q^{89} + 225 q^{91} - 504 q^{93} + 206 q^{95} - 224 q^{97} + O(q^{100}) \)

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

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