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Properties

Label 3100.3.fi
Level $3100$
Weight $3$
Character orbit 3100.fi
Rep. character $\chi_{3100}(409,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1280$
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.fi (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

\( 1280 q - 12 q^{5} + 500 q^{9} + O(q^{10}) \) \( 1280 q - 12 q^{5} + 500 q^{9} - 8 q^{25} + 90 q^{31} + 138 q^{35} + 45 q^{41} + 220 q^{45} + 70 q^{47} + 4520 q^{49} - 70 q^{51} - 225 q^{55} + 165 q^{59} + 216 q^{65} + 195 q^{67} - 80 q^{69} - 170 q^{71} + 60 q^{73} - 588 q^{75} + 1030 q^{81} + 900 q^{83} + 125 q^{87} - 946 q^{95} + 40 q^{97} + 840 q^{99} + O(q^{100}) \)

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

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