Defining parameters
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(1440\) | ||
Trace bound: | \(46\) | ||
Distinguishing \(T_p\): | \(11\), \(13\), \(17\), \(43\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 768 | 48 | 720 |
Cusp forms | 672 | 48 | 624 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
3150.2.b.a | $8$ | $25.153$ | 8.0.40960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}-q^{4}+(-\beta _{3}+\beta _{5})q^{7}-\beta _{1}q^{8}+\cdots\) |
3150.2.b.b | $8$ | $25.153$ | 8.0.40960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}-q^{4}+(-\beta _{3}-\beta _{5})q^{7}-\beta _{1}q^{8}+\cdots\) |
3150.2.b.c | $8$ | $25.153$ | 8.0.40960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}-q^{4}+(-\beta _{2}+\beta _{7})q^{7}-\beta _{1}q^{8}+\cdots\) |
3150.2.b.d | $8$ | $25.153$ | 8.0.40960000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}-q^{4}+(\beta _{3}+\beta _{5})q^{7}+\beta _{1}q^{8}+\cdots\) |
3150.2.b.e | $8$ | $25.153$ | 8.0.7442857984.4 | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q-\beta _{3}q^{2}-q^{4}-\beta _{6}q^{7}+\beta _{3}q^{8}+(-\beta _{5}+\cdots)q^{11}+\cdots\) |
3150.2.b.f | $8$ | $25.153$ | 8.0.7442857984.4 | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q-\beta _{3}q^{2}-q^{4}+\beta _{5}q^{7}+\beta _{3}q^{8}+(-\beta _{5}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)