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Properties

Label 2520.2.bj
Level $2520$
Weight $2$
Character orbit 2520.bj
Rep. character $\chi_{2520}(961,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $192$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2520.bj (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2520, [\chi])\).

Total New Old
Modular forms 1184 192 992
Cusp forms 1120 192 928
Eisenstein series 64 0 64

Trace form

\( 192 q + 8 q^{5} + 2 q^{9} + O(q^{10}) \) \( 192 q + 8 q^{5} + 2 q^{9} - 16 q^{17} - 22 q^{21} + 192 q^{25} + 6 q^{29} - 12 q^{31} + 8 q^{33} - 12 q^{39} - 2 q^{41} - 12 q^{43} - 6 q^{45} - 12 q^{47} - 12 q^{49} + 12 q^{51} - 8 q^{53} - 6 q^{61} - 28 q^{63} + 56 q^{69} + 56 q^{71} - 24 q^{77} + 34 q^{81} + 72 q^{83} - 92 q^{87} + 6 q^{89} + 12 q^{91} + 80 q^{93} + 52 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2520, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 3}\)