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Properties

Label 3100.3.ba
Level $3100$
Weight $3$
Character orbit 3100.ba
Rep. character $\chi_{3100}(1021,\cdot)$
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.ba (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

\( 640 q - 6 q^{5} - 4 q^{7} - 1890 q^{9} + O(q^{10}) \) \( 640 q - 6 q^{5} - 4 q^{7} - 1890 q^{9} + 20 q^{15} - 55 q^{23} + 48 q^{25} + 90 q^{31} - 102 q^{33} + 87 q^{35} - 205 q^{37} + 60 q^{41} - 90 q^{43} + 183 q^{45} + 18 q^{47} - 1140 q^{49} - 35 q^{51} - 50 q^{53} - 200 q^{55} + 55 q^{59} + 20 q^{63} - 585 q^{65} + 228 q^{67} + 200 q^{69} + 120 q^{71} - 60 q^{75} - 380 q^{77} - 550 q^{79} + 5280 q^{81} - 45 q^{85} - 81 q^{87} + 225 q^{91} + 441 q^{93} - 34 q^{95} + 286 q^{97} + O(q^{100}) \)

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

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