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Properties

Label 3100.3.fn
Level $3100$
Weight $3$
Character orbit 3100.fn
Rep. character $\chi_{3100}(21,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1280$
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.fn (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 7728 1280 6448
Cusp forms 7632 1280 6352
Eisenstein series 96 0 96

Trace form

\( 1280 q - 3 q^{5} - 32 q^{7} + 1890 q^{9} + O(q^{10}) \) \( 1280 q - 3 q^{5} - 32 q^{7} + 1890 q^{9} + 160 q^{15} + 55 q^{23} + 135 q^{25} - 90 q^{31} + 300 q^{33} - 171 q^{35} + 277 q^{37} + 30 q^{41} + 72 q^{43} + 69 q^{45} - 18 q^{47} + 960 q^{49} + 245 q^{51} + 122 q^{53} + 299 q^{55} + 288 q^{57} - 385 q^{59} - 20 q^{63} - 333 q^{65} + 294 q^{67} + 100 q^{69} + 330 q^{71} + 36 q^{73} - 69 q^{75} + 380 q^{77} + 250 q^{79} - 5280 q^{81} + 45 q^{83} + 45 q^{85} - 525 q^{87} - 225 q^{91} + 183 q^{93} - 86 q^{95} - 160 q^{97} + 840 q^{99} + O(q^{100}) \)

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

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