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Properties

Label 3100.3.dl
Level $3100$
Weight $3$
Character orbit 3100.dl
Rep. character $\chi_{3100}(157,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $768$
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.dl (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
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 7824 768 7056
Cusp forms 7536 768 6768
Eisenstein series 288 0 288

Trace form

\( 768 q + 4 q^{3} + 24 q^{7} + O(q^{10}) \) \( 768 q + 4 q^{3} + 24 q^{7} + 36 q^{21} + 62 q^{23} + 190 q^{27} + 84 q^{31} - 148 q^{33} - 244 q^{37} + 216 q^{41} - 168 q^{43} + 216 q^{47} - 112 q^{51} - 180 q^{53} - 52 q^{57} - 104 q^{61} - 304 q^{63} - 204 q^{67} - 432 q^{71} + 88 q^{73} - 612 q^{77} + 1704 q^{81} + 974 q^{83} - 268 q^{87} - 76 q^{91} + 132 q^{93} + 278 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3100, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(620, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1550, [\chi])\)\(^{\oplus 2}\)