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Properties

Label 207.7.d
Level $207$
Weight $7$
Character orbit 207.d
Rep. character $\chi_{207}(91,\cdot)$
Character field $\Q$
Dimension $59$
Newform subspaces $5$
Sturm bound $168$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 207.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(168\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(207, [\chi])\).

Total New Old
Modular forms 148 61 87
Cusp forms 140 59 81
Eisenstein series 8 2 6

Trace form

\( 59 q + 12 q^{2} + 1632 q^{4} + 465 q^{8} + O(q^{10}) \) \( 59 q + 12 q^{2} + 1632 q^{4} + 465 q^{8} + 2542 q^{13} + 40672 q^{16} - 11139 q^{23} - 167365 q^{25} + 19701 q^{26} + 21450 q^{29} + 17110 q^{31} + 159492 q^{32} + 81624 q^{35} - 349734 q^{41} + 1912 q^{46} + 202554 q^{47} - 903469 q^{49} - 845844 q^{50} + 232731 q^{52} - 847176 q^{55} - 34909 q^{58} - 591678 q^{59} - 322347 q^{62} + 1728299 q^{64} + 73848 q^{70} + 602178 q^{71} + 941614 q^{73} + 1645848 q^{77} - 785821 q^{82} + 248232 q^{85} + 4141836 q^{92} + 682931 q^{94} - 402144 q^{95} - 5479788 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(207, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
207.7.d.a 207.d 23.b $1$ $47.621$ \(\Q\) \(\Q(\sqrt{-23}) \) 23.7.b.a \(7\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+7q^{2}-15q^{4}-553q^{8}+1082q^{13}+\cdots\)
207.7.d.b 207.d 23.b $2$ $47.621$ \(\Q(\sqrt{69}) \) \(\Q(\sqrt{-23}) \) 23.7.b.b \(-7\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-3-\beta )q^{2}+(10^{2}+7\beta )q^{4}+(-1193+\cdots)q^{8}+\cdots\)
207.7.d.c 207.d 23.b $8$ $47.621$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 23.7.b.c \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{2}+(21-3\beta _{1}-\beta _{5})q^{4}+\cdots\)
207.7.d.d 207.d 23.b $24$ $47.621$ None 207.7.d.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
207.7.d.e 207.d 23.b $24$ $47.621$ None 69.7.d.a \(20\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{7}^{\mathrm{old}}(207, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(207, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)