Properties

Label 2012.2.e
Level $2012$
Weight $2$
Character orbit 2012.e
Rep. character $\chi_{2012}(9,\cdot)$
Character field $\Q(\zeta_{251})$
Dimension $10500$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 2012 = 2^{2} \cdot 503 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2012.e (of order \(251\) and degree \(250\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 503 \)
Character field: \(\Q(\zeta_{251})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2012, [\chi])\).

Total New Old
Modular forms 63750 10500 53250
Cusp forms 62250 10500 51750
Eisenstein series 1500 0 1500

Trace form

\( 10500 q + 2 q^{7} - 42 q^{9} + O(q^{10}) \) \( 10500 q + 2 q^{7} - 42 q^{9} + 2 q^{11} + 4 q^{13} + 8 q^{15} - 2 q^{17} - 2 q^{19} - 12 q^{21} - 4 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 6 q^{33} - 8 q^{35} + 8 q^{37} - 18 q^{39} - 8 q^{41} + 12 q^{43} - 18 q^{45} + 18 q^{47} - 32 q^{49} + 22 q^{51} + 2 q^{53} + 14 q^{55} + 2 q^{57} + 12 q^{59} + 14 q^{63} + 28 q^{65} + 4 q^{67} + 2 q^{69} - 6 q^{71} + 12 q^{73} + 4 q^{75} + 8 q^{77} + 18 q^{79} - 58 q^{81} - 4 q^{83} + 40 q^{85} + 2 q^{87} - 2 q^{89} - 6 q^{91} - 8 q^{93} + 30 q^{95} + 4 q^{97} + 36 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2012, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2012, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2012, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(503, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1006, [\chi])\)\(^{\oplus 2}\)