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Properties

Label 3100.3.bp
Level $3100$
Weight $3$
Character orbit 3100.bp
Rep. character $\chi_{3100}(829,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $640$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 3100.bp (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

\( 640 q - 5 q^{3} + 6 q^{5} - 475 q^{9} + O(q^{10}) \) \( 640 q - 5 q^{3} + 6 q^{5} - 475 q^{9} - 60 q^{15} - 45 q^{23} - 34 q^{25} - 35 q^{27} + 10 q^{31} + 115 q^{33} + 56 q^{35} - 115 q^{37} - 60 q^{41} + 90 q^{43} + 85 q^{45} + 10 q^{47} + 1200 q^{49} - 265 q^{51} + 100 q^{53} - 255 q^{55} - 480 q^{57} + 55 q^{59} + 240 q^{63} - 60 q^{65} - 195 q^{67} + 240 q^{69} - 300 q^{71} - 20 q^{73} - 695 q^{75} + 280 q^{77} - 1430 q^{81} + 595 q^{83} - 15 q^{85} + 90 q^{87} - 60 q^{93} - 62 q^{95} - 255 q^{97} + O(q^{100}) \)

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

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