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Properties

Label 630.3.cf
Level $630$
Weight $3$
Character orbit 630.cf
Rep. character $\chi_{630}(83,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $384$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 630.cf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(630, [\chi])\).

Total New Old
Modular forms 1184 384 800
Cusp forms 1120 384 736
Eisenstein series 64 0 64

Trace form

\( 384 q + O(q^{10}) \) \( 384 q + 72 q^{11} + 24 q^{15} + 768 q^{16} - 32 q^{18} - 24 q^{21} + 144 q^{23} + 192 q^{30} - 112 q^{36} + 160 q^{42} + 96 q^{46} + 576 q^{50} - 168 q^{51} - 144 q^{56} + 352 q^{57} - 96 q^{58} + 32 q^{60} - 324 q^{63} + 144 q^{65} - 128 q^{72} - 288 q^{77} - 256 q^{78} + 256 q^{81} + 288 q^{92} + 264 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(630, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(630, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(630, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)