↑

Properties

Label 270.4.r
Level $270$
Weight $4$
Character orbit 270.r
Rep. character $\chi_{270}(23,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $648$
Sturm bound $216$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 270.r (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(270, [\chi])\).

Total New Old
Modular forms 1992 648 1344
Cusp forms 1896 648 1248
Eisenstein series 96 0 96

Trace form

\( 648 q - 24 q^{6} + O(q^{10}) \) \( 648 q - 24 q^{6} - 48 q^{11} - 384 q^{20} + 312 q^{23} - 864 q^{25} + 444 q^{27} + 1008 q^{30} - 1056 q^{33} - 4968 q^{35} - 336 q^{36} + 72 q^{38} - 936 q^{41} + 1824 q^{42} + 2640 q^{45} + 3444 q^{47} + 384 q^{48} + 672 q^{50} + 6864 q^{51} - 1056 q^{56} - 4032 q^{57} + 108 q^{61} - 5208 q^{63} - 696 q^{65} - 7344 q^{67} - 1152 q^{68} + 384 q^{72} - 4356 q^{75} + 9840 q^{77} + 4272 q^{78} + 5808 q^{81} + 2820 q^{83} + 4176 q^{86} + 12276 q^{87} - 2496 q^{92} + 3072 q^{93} + 3540 q^{95} - 13824 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(270, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(270, [\chi])\) into lower level spaces

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