Properties

Label 28.7.h
Level $28$
Weight $7$
Character orbit 28.h
Rep. character $\chi_{28}(5,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $1$
Sturm bound $28$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 28.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(28, [\chi])\).

Total New Old
Modular forms 54 8 46
Cusp forms 42 8 34
Eisenstein series 12 0 12

Trace form

\( 8 q + 168 q^{5} - 452 q^{7} + 2004 q^{9} + O(q^{10}) \) \( 8 q + 168 q^{5} - 452 q^{7} + 2004 q^{9} - 540 q^{11} + 4056 q^{15} + 9912 q^{17} - 10836 q^{19} - 9612 q^{21} - 17832 q^{23} - 5272 q^{25} - 10632 q^{29} + 13524 q^{31} + 144396 q^{33} - 145956 q^{35} + 9164 q^{37} - 205524 q^{39} + 131456 q^{43} + 756252 q^{45} + 30156 q^{47} - 438352 q^{49} - 241860 q^{51} - 537060 q^{53} + 413496 q^{57} + 985992 q^{59} + 773220 q^{61} - 2228964 q^{63} - 266244 q^{65} - 988568 q^{67} + 74256 q^{71} + 2571156 q^{73} + 2230704 q^{75} - 2549880 q^{77} - 458984 q^{79} - 2816928 q^{81} + 1695192 q^{85} + 6079500 q^{87} - 439236 q^{89} - 2774472 q^{91} - 1808604 q^{93} - 3252768 q^{95} + 1963800 q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(28, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
28.7.h.a $8$ $6.442$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(168\) \(-452\) \(q+\beta _{3}q^{3}+(28-14\beta _{1}-\beta _{5})q^{5}+(-11^{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(28, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(28, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)