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Properties

Label 3012.2.q
Level $3012$
Weight $2$
Character orbit 3012.q
Rep. character $\chi_{3012}(25,\cdot)$
Character field $\Q(\zeta_{25})$
Dimension $840$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 3012 = 2^{2} \cdot 3 \cdot 251 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3012.q (of order \(25\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 251 \)
Character field: \(\Q(\zeta_{25})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3012, [\chi])\).

Total New Old
Modular forms 10200 840 9360
Cusp forms 9960 840 9120
Eisenstein series 240 0 240

Trace form

\( 840 q - 50 q^{7} + O(q^{10}) \) \( 840 q - 50 q^{7} + 20 q^{19} - 210 q^{25} + 40 q^{31} + 30 q^{35} - 30 q^{37} - 80 q^{39} - 10 q^{41} - 50 q^{49} + 20 q^{55} - 40 q^{59} - 10 q^{61} - 50 q^{65} - 30 q^{67} + 280 q^{71} - 20 q^{73} + 50 q^{77} + 10 q^{79} - 90 q^{83} - 10 q^{85} - 20 q^{89} + 20 q^{91} - 20 q^{93} + 120 q^{95} - 20 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3012, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3012, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3012, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(251, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(502, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(753, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1004, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1506, [\chi])\)\(^{\oplus 2}\)