Properties

Label 32.7.d
Level $32$
Weight $7$
Character orbit 32.d
Rep. character $\chi_{32}(15,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $2$
Sturm bound $28$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 32.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(28\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(32, [\chi])\).

Total New Old
Modular forms 28 7 21
Cusp forms 20 5 15
Eisenstein series 8 2 6

Trace form

\( 5 q + 2 q^{3} + 727 q^{9} + O(q^{10}) \) \( 5 q + 2 q^{3} + 727 q^{9} + 1362 q^{11} + 2442 q^{17} + 3938 q^{19} - 8275 q^{25} - 32860 q^{27} - 23500 q^{33} + 49920 q^{35} + 16698 q^{41} - 122542 q^{43} + 119765 q^{49} + 465412 q^{51} + 12500 q^{57} - 846990 q^{59} - 205440 q^{65} + 1386818 q^{67} - 149222 q^{73} - 2483950 q^{75} - 186839 q^{81} + 2786082 q^{83} + 403962 q^{89} - 3398400 q^{91} + 895978 q^{97} + 5702086 q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
32.7.d.a 32.d 8.d $1$ $7.362$ \(\Q\) \(\Q(\sqrt{-2}) \) \(0\) \(-46\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-46q^{3}+1387q^{9}+2338q^{11}-1726q^{17}+\cdots\)
32.7.d.b 32.d 8.d $4$ $7.362$ 4.0.3803625.2 None \(0\) \(48\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(12-\beta _{1})q^{3}-\beta _{2}q^{5}+(\beta _{2}-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(32, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)