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Properties

Label 252.9.g
Level $252$
Weight $9$
Character orbit 252.g
Rep. character $\chi_{252}(127,\cdot)$
Character field $\Q$
Dimension $120$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 252.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(252, [\chi])\).

Total New Old
Modular forms 392 120 272
Cusp forms 376 120 256
Eisenstein series 16 0 16

Trace form

\( 120 q + 3 q^{2} + 569 q^{4} - 336 q^{5} + 7839 q^{8} + O(q^{10}) \) \( 120 q + 3 q^{2} + 569 q^{4} - 336 q^{5} + 7839 q^{8} - 41972 q^{10} - 28560 q^{13} + 7203 q^{14} - 249707 q^{16} - 220752 q^{17} - 490812 q^{20} - 197008 q^{22} + 8489640 q^{25} - 615468 q^{26} - 74431 q^{28} + 997296 q^{29} - 5489457 q^{32} - 2061262 q^{34} + 2965616 q^{37} + 338310 q^{38} + 106400 q^{40} + 1409520 q^{41} - 10119540 q^{44} + 924828 q^{46} - 98825160 q^{49} + 34320765 q^{50} + 13718516 q^{52} - 3662160 q^{53} - 7109361 q^{56} - 26191130 q^{58} - 52013584 q^{61} + 81110316 q^{62} + 33787577 q^{64} - 12568224 q^{65} - 189562506 q^{68} - 11611236 q^{70} - 7651728 q^{73} + 193262946 q^{74} + 133820778 q^{76} - 47482176 q^{77} - 392786772 q^{80} - 103032790 q^{82} + 117712288 q^{85} + 327912492 q^{86} + 111400768 q^{88} + 100165296 q^{89} - 598956624 q^{92} - 422290092 q^{94} + 114327024 q^{97} - 2470629 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

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

Decomposition of \(S_{9}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)