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Properties

Label 3100.3.cb
Level $3100$
Weight $3$
Character orbit 3100.cb
Rep. character $\chi_{3100}(201,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $408$
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.cb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
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 3912 408 3504
Cusp forms 3768 408 3360
Eisenstein series 144 0 144

Trace form

\( 408 q + 18 q^{7} + 322 q^{9} + O(q^{10}) \) \( 408 q + 18 q^{7} + 322 q^{9} - 5 q^{11} + 15 q^{13} - 40 q^{17} + 38 q^{19} - 30 q^{21} - 10 q^{23} - 60 q^{27} - 10 q^{29} + 63 q^{31} + 35 q^{33} - 118 q^{39} - 79 q^{41} - 70 q^{43} - 48 q^{47} - 750 q^{49} + 250 q^{51} + 90 q^{53} - 230 q^{59} + 4 q^{63} - 24 q^{67} - 40 q^{69} + 8 q^{71} + 270 q^{73} + 285 q^{77} + 145 q^{79} - 869 q^{81} - 675 q^{83} + 680 q^{87} + 130 q^{89} - 615 q^{91} + 31 q^{93} - 284 q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(3100, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(124, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(620, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1550, [\chi])\)\(^{\oplus 2}\)