Properties

Label 16.14.a
Level $16$
Weight $14$
Character orbit 16.a
Rep. character $\chi_{16}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $5$
Sturm bound $28$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 16.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(28\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(16))\).

Total New Old
Modular forms 29 7 22
Cusp forms 23 6 17
Eisenstein series 6 1 5

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)Dim
\(+\)\(3\)
\(-\)\(3\)

Trace form

\( 6 q - 728 q^{3} + 16900 q^{5} + 65232 q^{7} + 2329966 q^{9} + O(q^{10}) \) \( 6 q - 728 q^{3} + 16900 q^{5} + 65232 q^{7} + 2329966 q^{9} - 7676680 q^{11} + 8510580 q^{13} - 32857232 q^{15} - 2730004 q^{17} + 265312968 q^{19} - 339269952 q^{21} + 210016880 q^{23} + 262952922 q^{25} - 2014719344 q^{27} + 765099348 q^{29} - 603156672 q^{31} + 7736141600 q^{33} + 2111687136 q^{35} - 17849283132 q^{37} + 21412862896 q^{39} - 24031840452 q^{41} - 36854217672 q^{43} + 40615936756 q^{45} + 48887008992 q^{47} + 62632236054 q^{49} - 174397305136 q^{51} + 54937343140 q^{53} + 273717035856 q^{55} - 211899133472 q^{57} - 665598610984 q^{59} - 179422666476 q^{61} + 2048602666896 q^{63} - 181937377544 q^{65} - 2913745375320 q^{67} + 634653457472 q^{69} + 3548344800592 q^{71} + 1333995927036 q^{73} - 6534790174888 q^{75} - 1607022622656 q^{77} + 8324451839520 q^{79} - 65260268522 q^{81} - 13365043595960 q^{83} + 193493289288 q^{85} + 25789862820912 q^{87} - 3034933603620 q^{89} - 29340278911392 q^{91} - 575802029312 q^{93} + 39035988899632 q^{95} + 6262475466828 q^{97} - 54378142955752 q^{99} + O(q^{100}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(16))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2
16.14.a.a 16.a 1.a $1$ $17.157$ \(\Q\) None \(0\) \(-1236\) \(-57450\) \(-64232\) $-$ $\mathrm{SU}(2)$ \(q-1236q^{3}-57450q^{5}-64232q^{7}+\cdots\)
16.14.a.b 16.a 1.a $1$ $17.157$ \(\Q\) None \(0\) \(-468\) \(56214\) \(-333032\) $-$ $\mathrm{SU}(2)$ \(q-468q^{3}+56214q^{5}-333032q^{7}+\cdots\)
16.14.a.c 16.a 1.a $1$ $17.157$ \(\Q\) None \(0\) \(12\) \(-4330\) \(139992\) $+$ $\mathrm{SU}(2)$ \(q+12q^{3}-4330q^{5}+139992q^{7}+\cdots\)
16.14.a.d 16.a 1.a $1$ $17.157$ \(\Q\) None \(0\) \(1836\) \(3990\) \(433432\) $-$ $\mathrm{SU}(2)$ \(q+1836q^{3}+3990q^{5}+433432q^{7}+\cdots\)
16.14.a.e 16.a 1.a $2$ $17.157$ \(\Q(\sqrt{781}) \) None \(0\) \(-872\) \(18476\) \(-110928\) $+$ $\mathrm{SU}(2)$ \(q+(-436-\beta )q^{3}+(9238+12\beta )q^{5}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(16))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(16)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)