Properties

Label 630.4.ca
Level $630$
Weight $4$
Character orbit 630.ca
Rep. character $\chi_{630}(113,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $432$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 630.ca (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(630, [\chi])\).

Total New Old
Modular forms 1760 432 1328
Cusp forms 1696 432 1264
Eisenstein series 64 0 64

Trace form

\( 432 q + 16 q^{3} + O(q^{10}) \) \( 432 q + 16 q^{3} - 48 q^{11} - 64 q^{12} - 8 q^{15} + 3456 q^{16} - 16 q^{18} + 384 q^{20} + 224 q^{21} + 312 q^{23} - 576 q^{25} + 592 q^{27} - 1816 q^{33} + 256 q^{36} + 576 q^{37} + 144 q^{38} + 3072 q^{41} + 3520 q^{45} + 6888 q^{47} + 512 q^{48} - 5224 q^{51} + 3168 q^{55} - 104 q^{57} + 1440 q^{60} - 1064 q^{63} - 696 q^{65} + 1888 q^{66} + 2448 q^{67} - 128 q^{72} - 392 q^{75} - 2464 q^{78} - 960 q^{81} - 7488 q^{82} + 5640 q^{83} - 3312 q^{85} + 8352 q^{86} + 9920 q^{87} + 2960 q^{90} + 2016 q^{91} + 1248 q^{92} + 2824 q^{93} + 7080 q^{95} + 3024 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(630, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(630, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)