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Properties

Label 3100.3.dm
Level $3100$
Weight $3$
Character orbit 3100.dm
Rep. character $\chi_{3100}(597,\cdot)$
Character field $\Q(\zeta_{20})$
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.dm (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
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 7728 1280 6448
Cusp forms 7632 1280 6352
Eisenstein series 96 0 96

Trace form

\( 1280 q + 6 q^{3} + 16 q^{7} + 50 q^{9} + O(q^{10}) \) \( 1280 q + 6 q^{3} + 16 q^{7} + 50 q^{9} + 104 q^{15} - 62 q^{23} + 76 q^{25} - 30 q^{27} + 200 q^{29} + 258 q^{33} + 228 q^{35} - 266 q^{37} - 12 q^{43} - 138 q^{45} - 366 q^{47} + 60 q^{53} + 550 q^{55} - 428 q^{57} + 250 q^{59} - 316 q^{63} + 184 q^{65} - 186 q^{67} - 120 q^{71} - 88 q^{73} - 962 q^{75} + 132 q^{77} + 2810 q^{81} + 186 q^{83} - 436 q^{85} + 448 q^{87} - 212 q^{93} + 664 q^{95} - 68 q^{97} + O(q^{100}) \)

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

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