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Properties

Label 3100.3.bo
Level $3100$
Weight $3$
Character orbit 3100.bo
Rep. character $\chi_{3100}(89,\cdot)$
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.bo (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

\( 640 q + 6 q^{5} + 20 q^{7} - 500 q^{9} + O(q^{10}) \) \( 640 q + 6 q^{5} + 20 q^{7} - 500 q^{9} + 36 q^{25} + 45 q^{27} + 10 q^{31} - 44 q^{35} + 115 q^{37} + 15 q^{41} - 90 q^{43} - 205 q^{45} + 115 q^{47} + 1100 q^{49} + 35 q^{51} + 170 q^{53} + 180 q^{55} + 350 q^{57} - 20 q^{59} - 240 q^{63} - 360 q^{65} - 160 q^{69} - 150 q^{71} - 20 q^{73} + 185 q^{75} + 140 q^{77} + 650 q^{79} - 1255 q^{81} + 15 q^{83} + 150 q^{85} - 515 q^{87} + 75 q^{89} + 725 q^{93} - 47 q^{95} + 505 q^{97} + O(q^{100}) \)

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

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