Defining parameters
Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3332.cc (of order \(42\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3332 \) |
Character field: | \(\Q(\zeta_{42})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(504\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3332, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 96 | 96 | 0 |
Cusp forms | 48 | 48 | 0 |
Eisenstein series | 48 | 48 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 48 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3332, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3332.1.cc.a | $12$ | $1.663$ | \(\Q(\zeta_{21})\) | $D_{21}$ | \(\Q(\sqrt{-17}) \) | None | \(1\) | \(-13\) | \(0\) | \(2\) | \(q-\zeta_{42}^{17}q^{2}+(-1+\zeta_{42}^{11})q^{3}-\zeta_{42}^{13}q^{4}+\cdots\) |
3332.1.cc.b | $12$ | $1.663$ | \(\Q(\zeta_{21})\) | $D_{21}$ | \(\Q(\sqrt{-17}) \) | None | \(1\) | \(13\) | \(0\) | \(-2\) | \(q-\zeta_{42}^{17}q^{2}+(1-\zeta_{42}^{11})q^{3}-\zeta_{42}^{13}q^{4}+\cdots\) |
3332.1.cc.c | $24$ | $1.663$ | \(\Q(\zeta_{84})\) | $D_{42}$ | \(\Q(\sqrt{-17}) \) | None | \(-2\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{84}^{40}q^{2}+(\zeta_{84}^{21}-\zeta_{84}^{37})q^{3}+\cdots\) |