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Properties

Label 3020.2.bg
Level $3020$
Weight $2$
Character orbit 3020.bg
Rep. character $\chi_{3020}(581,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $400$
Sturm bound $912$

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Defining parameters

Level: \( N \) \(=\) \( 3020 = 2^{2} \cdot 5 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3020.bg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 151 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(912\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3020, [\chi])\).

Total New Old
Modular forms 3696 400 3296
Cusp forms 3600 400 3200
Eisenstein series 96 0 96

Trace form

\( 400 q + 4 q^{3} - 92 q^{9} + O(q^{10}) \) \( 400 q + 4 q^{3} - 92 q^{9} - 6 q^{11} + 2 q^{13} - 2 q^{15} - 38 q^{17} - 8 q^{19} - 6 q^{21} + 10 q^{23} + 50 q^{25} + 10 q^{27} - 26 q^{29} + 14 q^{31} + 38 q^{33} - 16 q^{35} - 4 q^{37} - 106 q^{39} + 10 q^{41} - 18 q^{43} - 14 q^{47} + 64 q^{49} + 56 q^{51} + 8 q^{53} + 12 q^{55} - 16 q^{59} + 38 q^{61} + 130 q^{63} + 20 q^{65} + 40 q^{67} + 140 q^{69} - 48 q^{71} - 4 q^{73} + 8 q^{75} - 134 q^{77} + 24 q^{79} - 28 q^{81} + 2 q^{83} + 10 q^{85} + 48 q^{87} + 14 q^{89} - 32 q^{91} - 210 q^{93} + 8 q^{95} - 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3020, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3020, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3020, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(151, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(302, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(604, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(755, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1510, [\chi])\)\(^{\oplus 2}\)