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Properties

Label 1350.4.bb
Level $1350$
Weight $4$
Character orbit 1350.bb
Rep. character $\chi_{1350}(257,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1944$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1350.bb (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1350, [\chi])\).

Total New Old
Modular forms 9864 1944 7920
Cusp forms 9576 1944 7632
Eisenstein series 288 0 288

Trace form

\( 1944 q + 48 q^{6} + O(q^{10}) \) \( 1944 q + 48 q^{6} + 96 q^{11} - 312 q^{23} - 444 q^{27} + 1056 q^{33} + 672 q^{36} - 72 q^{38} + 1872 q^{41} - 1824 q^{42} - 3444 q^{47} - 384 q^{48} + 3192 q^{51} + 2112 q^{56} + 4032 q^{57} - 216 q^{61} + 5208 q^{63} + 7344 q^{67} + 1152 q^{68} - 384 q^{72} - 9840 q^{77} - 4272 q^{78} - 11616 q^{81} - 2820 q^{83} + 2088 q^{86} - 12276 q^{87} + 2496 q^{92} - 3072 q^{93} + 13824 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1350, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1350, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)