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Properties

Label 912.3.m
Level $912$
Weight $3$
Character orbit 912.m
Rep. character $\chi_{912}(799,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $3$
Sturm bound $480$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 912.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(480\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(912, [\chi])\).

Total New Old
Modular forms 332 36 296
Cusp forms 308 36 272
Eisenstein series 24 0 24

Trace form

\( 36 q - 24 q^{5} - 108 q^{9} + O(q^{10}) \) \( 36 q - 24 q^{5} - 108 q^{9} + 72 q^{13} + 24 q^{17} + 156 q^{25} - 120 q^{29} - 144 q^{33} - 24 q^{37} + 120 q^{41} + 72 q^{45} - 12 q^{49} + 168 q^{53} - 120 q^{61} - 144 q^{65} - 408 q^{73} - 48 q^{77} + 324 q^{81} + 96 q^{85} + 120 q^{89} + 264 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
912.3.m.a 912.m 4.b $12$ $24.850$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 912.3.m.a \(0\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{3}+(-1-\beta _{3})q^{5}+(-\beta _{6}-\beta _{11})q^{7}+\cdots\)
912.3.m.b 912.m 4.b $12$ $24.850$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 912.3.m.b \(0\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(-1-\beta _{2})q^{5}+\beta _{10}q^{7}+\cdots\)
912.3.m.c 912.m 4.b $12$ $24.850$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 912.3.m.c \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{3}-\beta _{4}q^{5}+\beta _{7}q^{7}-3q^{9}+(2\beta _{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(912, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)