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Properties

Label 1014.2.r
Level $1014$
Weight $2$
Character orbit 1014.r
Rep. character $\chi_{1014}(5,\cdot)$
Character field $\Q(\zeta_{52})$
Dimension $1488$
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.r (of order \(52\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 507 \)
Character field: \(\Q(\zeta_{52})\)
Sturm bound: \(364\)

Dimensions

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

Total New Old
Modular forms 4464 1488 2976
Cusp forms 4272 1488 2784
Eisenstein series 192 0 192

Trace form

\( 1488 q + 12 q^{7} + O(q^{10}) \) \( 1488 q + 12 q^{7} + 124 q^{16} + 12 q^{19} + 24 q^{27} - 12 q^{28} - 104 q^{30} - 12 q^{31} - 36 q^{33} - 12 q^{37} - 104 q^{39} - 24 q^{42} + 224 q^{45} - 12 q^{52} + 36 q^{54} - 88 q^{55} + 36 q^{57} + 16 q^{61} - 224 q^{63} - 16 q^{66} + 220 q^{67} + 208 q^{70} + 12 q^{73} - 260 q^{75} + 12 q^{76} + 36 q^{78} - 80 q^{79} - 16 q^{81} + 72 q^{85} - 32 q^{87} + 12 q^{91} + 224 q^{93} + 64 q^{94} + 60 q^{97} - 36 q^{99} + O(q^{100}) \)

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

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