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Properties

Label 450.4.p
Level $450$
Weight $4$
Character orbit 450.p
Rep. character $\chi_{450}(257,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $216$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 450.p (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(450, [\chi])\).

Total New Old
Modular forms 1128 216 912
Cusp forms 1032 216 816
Eisenstein series 96 0 96

Trace form

\( 216 q + 8 q^{3} - 32 q^{6} + O(q^{10}) \) \( 216 q + 8 q^{3} - 32 q^{6} - 96 q^{11} - 32 q^{12} + 1728 q^{16} - 16 q^{18} + 928 q^{21} + 312 q^{23} - 244 q^{27} - 268 q^{33} + 64 q^{36} + 288 q^{37} + 72 q^{38} + 5544 q^{41} + 952 q^{42} - 2016 q^{46} + 3444 q^{47} + 256 q^{48} - 424 q^{51} - 2112 q^{56} - 3064 q^{57} + 504 q^{58} + 72 q^{61} - 3940 q^{63} + 2008 q^{66} + 1224 q^{67} - 1152 q^{68} - 128 q^{72} - 9744 q^{77} + 192 q^{78} + 6824 q^{81} - 3744 q^{82} + 2820 q^{83} - 2088 q^{86} + 4952 q^{87} + 4032 q^{91} + 1248 q^{92} + 7364 q^{93} - 256 q^{96} + 1512 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(450, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)