Properties

Label 14.14.a
Level $14$
Weight $14$
Character orbit 14.a
Rep. character $\chi_{14}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $28$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 14.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(28\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 28 6 22
Cusp forms 24 6 18
Eisenstein series 4 0 4

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

\(2\)\(7\)FrickeDim
\(+\)\(+\)$+$\(1\)
\(+\)\(-\)$-$\(2\)
\(-\)\(+\)$-$\(2\)
\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(4\)

Trace form

\( 6 q + 2658 q^{3} + 24576 q^{4} + 75454 q^{5} - 159872 q^{6} - 54334 q^{9} + O(q^{10}) \) \( 6 q + 2658 q^{3} + 24576 q^{4} + 75454 q^{5} - 159872 q^{6} - 54334 q^{9} + 5391744 q^{10} - 4198900 q^{11} + 10887168 q^{12} - 21536910 q^{13} - 15059072 q^{14} + 74652440 q^{15} + 100663296 q^{16} + 127703888 q^{17} + 109790976 q^{18} + 356289702 q^{19} + 309059584 q^{20} - 330123094 q^{21} - 429056256 q^{22} + 2583845000 q^{23} - 654835712 q^{24} + 803490486 q^{25} - 211760000 q^{26} + 2993080284 q^{27} - 116007344 q^{29} + 3944153600 q^{30} - 16892503572 q^{31} - 4033651040 q^{33} - 2957779200 q^{34} - 330123094 q^{35} - 222552064 q^{36} - 6687870048 q^{37} - 20960621952 q^{38} - 83596016032 q^{39} + 22084583424 q^{40} + 63713977272 q^{41} - 10978063488 q^{42} - 77765105388 q^{43} - 17198694400 q^{44} + 62435143798 q^{45} - 4846932480 q^{46} + 372645466836 q^{47} + 44593840128 q^{48} + 83047723206 q^{49} - 121923762944 q^{50} - 269390050820 q^{51} - 88215183360 q^{52} - 255705729036 q^{53} + 519469197568 q^{54} + 317621938296 q^{55} - 61681958912 q^{56} + 395214315276 q^{57} + 69342181632 q^{58} - 712642478042 q^{59} + 305776394240 q^{60} + 1774004468670 q^{61} - 196641183488 q^{62} - 576231154716 q^{63} + 412316860416 q^{64} - 2223781083804 q^{65} - 1854843428864 q^{66} - 3537401376576 q^{67} + 523075125248 q^{68} + 1675209451120 q^{69} - 1051228639104 q^{70} + 2331418655096 q^{71} + 449703837696 q^{72} - 1394414740956 q^{73} - 2823317149440 q^{74} + 6299688623990 q^{75} + 1459362619392 q^{76} - 1891936628204 q^{77} + 2281850355712 q^{78} - 4214235906456 q^{79} + 1265908056064 q^{80} - 5400214549582 q^{81} + 1312824627456 q^{82} - 2760602952178 q^{83} - 1352184193024 q^{84} + 13991004814908 q^{85} + 258030341376 q^{86} + 5224716578852 q^{87} - 1757414424576 q^{88} + 11243600567052 q^{89} + 6698734949248 q^{90} - 1445221257522 q^{91} + 10583429120000 q^{92} - 25415783886232 q^{93} - 9467660368128 q^{94} + 20345555963960 q^{95} - 2682207076352 q^{96} - 10215598221168 q^{97} - 10722640750564 q^{99} + O(q^{100}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(14))\) 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 7
14.14.a.a 14.a 1.a $1$ $15.012$ \(\Q\) None \(-64\) \(1626\) \(-36400\) \(-117649\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+1626q^{3}+2^{12}q^{4}-36400q^{5}+\cdots\)
14.14.a.b 14.a 1.a $1$ $15.012$ \(\Q\) None \(64\) \(-1026\) \(4320\) \(117649\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}-1026q^{3}+2^{12}q^{4}+4320q^{5}+\cdots\)
14.14.a.c 14.a 1.a $2$ $15.012$ \(\Q(\sqrt{100129}) \) None \(-128\) \(952\) \(32004\) \(235298\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{6}q^{2}+(476-\beta )q^{3}+2^{12}q^{4}+(16002+\cdots)q^{5}+\cdots\)
14.14.a.d 14.a 1.a $2$ $15.012$ \(\Q(\sqrt{78985}) \) None \(128\) \(1106\) \(75530\) \(-235298\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{6}q^{2}+(553-5\beta )q^{3}+2^{12}q^{4}+\cdots\)

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

\( S_{14}^{\mathrm{old}}(\Gamma_0(14)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)