Defining parameters
Level: | \( N \) | \(=\) | \( 100 = 2^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 100.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(100, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 54 | 4 | 50 |
Cusp forms | 36 | 4 | 32 |
Eisenstein series | 18 | 0 | 18 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(100, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
100.4.c.a | $2$ | $5.900$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2iq^{3}+8iq^{7}+11q^{9}-60q^{11}+\cdots\) |
100.4.c.b | $2$ | $5.900$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}-26iq^{7}+26q^{9}+45q^{11}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(100, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(100, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)