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Properties

Label 3100.3.dj
Level $3100$
Weight $3$
Character orbit 3100.dj
Rep. character $\chi_{3100}(373,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1200$
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.dj (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
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 1200 6528
Cusp forms 7632 1200 6432
Eisenstein series 96 0 96

Trace form

\( 1200 q - 12 q^{5} - 12 q^{7} + O(q^{10}) \) \( 1200 q - 12 q^{5} - 12 q^{7} + 36 q^{13} - 12 q^{15} - 136 q^{17} - 200 q^{19} - 64 q^{23} + 48 q^{25} + 84 q^{27} + 308 q^{33} + 284 q^{35} + 76 q^{37} + 800 q^{39} - 160 q^{41} + 108 q^{43} + 440 q^{45} - 52 q^{47} - 428 q^{53} - 80 q^{55} - 1260 q^{57} + 240 q^{61} - 1860 q^{63} - 60 q^{65} - 384 q^{67} + 68 q^{73} + 464 q^{75} + 52 q^{77} + 2700 q^{81} + 644 q^{83} + 1176 q^{85} + 1196 q^{87} + 1600 q^{89} + 352 q^{95} + 64 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3100, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1550, [\chi])\)\(^{\oplus 2}\)