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Properties

Label 3100.3.cr
Level $3100$
Weight $3$
Character orbit 3100.cr
Rep. character $\chi_{3100}(893,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $384$
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.cr (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(3100, [\chi])\).

Total New Old
Modular forms 3912 384 3528
Cusp forms 3768 384 3384
Eisenstein series 144 0 144

Trace form

\( 384 q + 4 q^{3} + 8 q^{7} + O(q^{10}) \) \( 384 q + 4 q^{3} + 8 q^{7} + 12 q^{21} - 28 q^{23} - 104 q^{27} - 12 q^{31} - 40 q^{33} + 104 q^{37} + 104 q^{41} + 84 q^{43} - 104 q^{47} - 112 q^{51} + 112 q^{53} + 236 q^{57} - 104 q^{61} - 164 q^{63} + 102 q^{67} - 44 q^{71} + 104 q^{73} + 148 q^{77} + 2472 q^{81} - 232 q^{83} - 94 q^{87} + 264 q^{91} + 212 q^{93} - 436 q^{97} + O(q^{100}) \)

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

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