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Properties

Label 3100.3.cm
Level $3100$
Weight $3$
Character orbit 3100.cm
Rep. character $\chi_{3100}(61,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $640$
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.cm (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 3864 640 3224
Cusp forms 3816 640 3176
Eisenstein series 48 0 48

Trace form

\( 640 q + 24 q^{5} + 16 q^{7} + 460 q^{9} + O(q^{10}) \) \( 640 q + 24 q^{5} + 16 q^{7} + 460 q^{9} - 12 q^{25} + 90 q^{31} - 92 q^{33} - 78 q^{35} - 90 q^{41} - 322 q^{45} - 42 q^{47} + 4560 q^{49} + 140 q^{51} + 330 q^{59} - 220 q^{63} - 282 q^{67} - 100 q^{69} + 220 q^{71} - 1570 q^{81} + 54 q^{87} - 754 q^{93} + 6 q^{95} - 684 q^{97} + O(q^{100}) \)

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

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