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Properties

Label 1014.2.m
Level $1014$
Weight $2$
Character orbit 1014.m
Rep. character $\chi_{1014}(79,\cdot)$
Character field $\Q(\zeta_{13})$
Dimension $336$
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.m (of order \(13\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{13})\)
Sturm bound: \(364\)

Dimensions

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

Total New Old
Modular forms 2232 336 1896
Cusp forms 2136 336 1800
Eisenstein series 96 0 96

Trace form

\( 336 q + 2 q^{2} + 2 q^{3} - 28 q^{4} + 4 q^{5} + 4 q^{7} + 2 q^{8} - 28 q^{9} + O(q^{10}) \) \( 336 q + 2 q^{2} + 2 q^{3} - 28 q^{4} + 4 q^{5} + 4 q^{7} + 2 q^{8} - 28 q^{9} + 8 q^{10} + 16 q^{11} + 2 q^{12} - 14 q^{13} + 8 q^{14} + 8 q^{15} - 28 q^{16} + 12 q^{17} + 2 q^{18} + 28 q^{19} + 4 q^{20} + 12 q^{21} - 48 q^{22} + 16 q^{23} - 4 q^{25} + 14 q^{26} + 2 q^{27} + 4 q^{28} + 12 q^{29} + 4 q^{30} - 16 q^{31} + 2 q^{32} + 8 q^{33} + 20 q^{34} + 32 q^{35} - 28 q^{36} + 40 q^{37} + 8 q^{38} + 14 q^{39} - 18 q^{40} + 52 q^{41} + 4 q^{42} + 32 q^{43} + 16 q^{44} + 4 q^{45} + 24 q^{46} + 40 q^{47} + 2 q^{48} - 44 q^{49} + 30 q^{50} + 12 q^{51} + 12 q^{52} - 78 q^{53} - 32 q^{55} + 8 q^{56} + 12 q^{57} - 16 q^{58} + 56 q^{59} - 44 q^{60} + 52 q^{61} + 24 q^{62} + 4 q^{63} - 28 q^{64} + 76 q^{65} + 16 q^{66} - 72 q^{67} + 12 q^{68} + 16 q^{69} - 152 q^{70} - 76 q^{71} + 2 q^{72} + 72 q^{73} - 146 q^{74} + 30 q^{75} - 24 q^{76} + 104 q^{77} + 12 q^{78} + 52 q^{79} + 4 q^{80} - 28 q^{81} + 28 q^{82} + 72 q^{83} + 12 q^{84} - 26 q^{85} - 108 q^{86} - 20 q^{87} + 4 q^{88} + 76 q^{89} + 8 q^{90} - 4 q^{91} + 16 q^{92} - 154 q^{93} - 4 q^{94} - 88 q^{95} - 68 q^{97} + 66 q^{98} + 16 q^{99} + O(q^{100}) \)

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

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