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Properties

Label 1014.2.p
Level $1014$
Weight $2$
Character orbit 1014.p
Rep. character $\chi_{1014}(25,\cdot)$
Character field $\Q(\zeta_{26})$
Dimension $360$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.p (of order \(26\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{26})\)
Sturm bound: \(364\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1014, [\chi])\).

Total New Old
Modular forms 2232 360 1872
Cusp forms 2136 360 1776
Eisenstein series 96 0 96

Trace form

\( 360 q - 2 q^{3} + 30 q^{4} - 30 q^{9} + O(q^{10}) \) \( 360 q - 2 q^{3} + 30 q^{4} - 30 q^{9} + 4 q^{10} + 2 q^{12} + 32 q^{13} - 8 q^{14} - 30 q^{16} + 8 q^{17} + 48 q^{22} + 34 q^{25} - 4 q^{26} - 2 q^{27} + 8 q^{29} + 4 q^{30} + 52 q^{31} - 16 q^{35} + 30 q^{36} - 8 q^{38} + 6 q^{39} - 4 q^{40} - 4 q^{42} - 2 q^{48} + 86 q^{49} + 12 q^{51} - 6 q^{52} + 104 q^{53} - 8 q^{55} + 8 q^{56} + 52 q^{58} - 52 q^{60} - 16 q^{61} + 24 q^{62} + 30 q^{64} - 8 q^{65} - 52 q^{67} - 8 q^{68} + 156 q^{71} - 36 q^{74} - 2 q^{75} + 52 q^{76} + 8 q^{77} - 4 q^{78} - 20 q^{79} - 30 q^{81} + 24 q^{82} - 104 q^{85} - 156 q^{86} + 68 q^{87} + 4 q^{88} + 4 q^{90} + 112 q^{91} + 182 q^{93} + 20 q^{94} + 200 q^{95} - 156 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1014, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1014, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1014, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)