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Properties

Label 306.2.l
Level $306$
Weight $2$
Character orbit 306.l
Rep. character $\chi_{306}(19,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $28$
Newform subspaces $5$
Sturm bound $108$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 306 = 2 \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 306.l (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 5 \)
Sturm bound: \(108\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(306, [\chi])\).

Total New Old
Modular forms 248 28 220
Cusp forms 184 28 156
Eisenstein series 64 0 64

Trace form

\( 28 q - 8 q^{5} + O(q^{10}) \) \( 28 q - 8 q^{5} + 12 q^{11} + 8 q^{14} - 28 q^{16} + 8 q^{19} + 8 q^{22} + 32 q^{23} + 8 q^{25} - 8 q^{26} - 8 q^{28} + 16 q^{34} + 32 q^{35} - 8 q^{37} - 32 q^{41} + 12 q^{43} - 24 q^{44} - 48 q^{49} - 44 q^{50} - 24 q^{52} - 56 q^{53} - 12 q^{59} - 16 q^{61} - 48 q^{65} + 8 q^{67} + 16 q^{70} + 56 q^{71} + 40 q^{73} + 8 q^{74} - 8 q^{76} + 56 q^{77} - 8 q^{79} + 8 q^{80} + 12 q^{82} + 4 q^{83} - 96 q^{85} + 56 q^{86} - 28 q^{88} - 16 q^{94} - 16 q^{95} - 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(306, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
306.2.l.a 306.l 17.d $4$ $2.443$ \(\Q(\zeta_{8})\) None 306.2.l.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-1+\zeta_{8})q^{5}+\cdots\)
306.2.l.b 306.l 17.d $4$ $2.443$ \(\Q(\zeta_{8})\) None 306.2.l.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1-\zeta_{8})q^{5}+(-2\zeta_{8}+\cdots)q^{7}+\cdots\)
306.2.l.c 306.l 17.d $4$ $2.443$ \(\Q(\zeta_{8})\) None 34.2.d.a \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(2-2\zeta_{8})q^{5}+\cdots\)
306.2.l.d 306.l 17.d $8$ $2.443$ \(\Q(\zeta_{16})\) None 102.2.h.a \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q-\zeta_{16}^{4}q^{2}-\zeta_{16}^{2}q^{4}+(-1-\zeta_{16}+\cdots)q^{5}+\cdots\)
306.2.l.e 306.l 17.d $8$ $2.443$ \(\Q(\zeta_{16})\) None 102.2.h.b \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q-\zeta_{16}^{4}q^{2}-\zeta_{16}^{2}q^{4}+(-1+\zeta_{16}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(306, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(306, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 2}\)