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Properties

Label 144.12.l
Level $144$
Weight $12$
Character orbit 144.l
Rep. character $\chi_{144}(35,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $176$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 144.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(144, [\chi])\).

Total New Old
Modular forms 536 176 360
Cusp forms 520 176 344
Eisenstein series 16 0 16

Trace form

\( 176 q + O(q^{10}) \) \( 176 q - 1075000 q^{10} + 13095280 q^{16} - 22582576 q^{19} - 74321144 q^{22} + 302069832 q^{28} + 342697320 q^{34} - 6526795512 q^{40} - 4763690656 q^{43} - 6375553864 q^{46} + 49715643824 q^{49} - 18274685064 q^{52} + 38245610944 q^{55} + 28442299560 q^{58} + 4301654048 q^{61} + 39894936528 q^{64} - 20282756048 q^{67} + 35110598184 q^{70} - 128711746176 q^{76} + 327605911600 q^{82} + 168955700000 q^{85} + 139328369712 q^{88} + 209413389552 q^{91} + 184166545176 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

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

Decomposition of \(S_{12}^{\mathrm{old}}(144, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(144, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)