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Properties

Label 14.10.a
Level $14$
Weight $10$
Character orbit 14.a
Rep. character $\chi_{14}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $20$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 14.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(20\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(14))\).

Total New Old
Modular forms 20 4 16
Cusp forms 16 4 12
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
\(+\)\(+\)$+$\(1\)
\(+\)\(-\)$-$\(2\)
\(-\)\(+\)$-$\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(3\)

Trace form

\( 4 q - 32 q^{2} + 150 q^{3} + 1024 q^{4} - 1626 q^{5} + 3040 q^{6} - 8192 q^{8} + 65552 q^{9} + O(q^{10}) \) \( 4 q - 32 q^{2} + 150 q^{3} + 1024 q^{4} - 1626 q^{5} + 3040 q^{6} - 8192 q^{8} + 65552 q^{9} + 43424 q^{10} + 39612 q^{11} + 38400 q^{12} - 28766 q^{13} - 76832 q^{14} + 592280 q^{15} + 262144 q^{16} - 885564 q^{17} - 753888 q^{18} + 49442 q^{19} - 416256 q^{20} - 427378 q^{21} + 928576 q^{22} - 2656200 q^{23} + 778240 q^{24} - 1443504 q^{25} - 47776 q^{26} - 3413052 q^{27} + 9137868 q^{29} - 6517120 q^{30} + 3350596 q^{31} - 2097152 q^{32} + 32512912 q^{33} + 13483648 q^{34} - 9205434 q^{35} + 16781312 q^{36} - 36564244 q^{37} - 23716192 q^{38} - 7908112 q^{39} + 11116544 q^{40} + 34564860 q^{41} - 6223392 q^{42} + 13013012 q^{43} + 10140672 q^{44} - 116480402 q^{45} - 36540800 q^{46} + 34924380 q^{47} + 9830400 q^{48} + 23059204 q^{49} - 29933984 q^{50} - 34235276 q^{51} - 7364096 q^{52} - 46913208 q^{53} - 2326208 q^{54} + 36542536 q^{55} - 19668992 q^{56} + 183244164 q^{57} + 31612544 q^{58} - 108522318 q^{59} + 151623680 q^{60} + 76257142 q^{61} + 131969600 q^{62} + 207475212 q^{63} + 67108864 q^{64} - 230680044 q^{65} - 254604032 q^{66} + 580211352 q^{67} - 226704384 q^{68} - 254285600 q^{69} + 105490336 q^{70} + 16036680 q^{71} - 192995328 q^{72} - 142210704 q^{73} + 460406144 q^{74} - 1606313950 q^{75} + 12657152 q^{76} + 120693468 q^{77} + 40164352 q^{78} + 635427112 q^{79} - 106561536 q^{80} + 540236888 q^{81} - 756585216 q^{82} - 134458710 q^{83} - 109408768 q^{84} + 1026034348 q^{85} - 806649664 q^{86} - 1833076660 q^{87} + 237715456 q^{88} + 156632808 q^{89} + 2024135968 q^{90} + 550621330 q^{91} - 679987200 q^{92} + 91836440 q^{93} + 1250460096 q^{94} + 362338680 q^{95} + 199229440 q^{96} - 118654428 q^{97} - 184473632 q^{98} + 2882415692 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(14))\) 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
14.10.a.a 14.a 1.a $1$ $7.211$ \(\Q\) None \(-16\) \(-6\) \(560\) \(-2401\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}-6q^{3}+2^{8}q^{4}+560q^{5}+\cdots\)
14.10.a.b 14.a 1.a $1$ $7.211$ \(\Q\) None \(16\) \(170\) \(544\) \(-2401\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}+170q^{3}+2^{8}q^{4}+544q^{5}+\cdots\)
14.10.a.c 14.a 1.a $2$ $7.211$ \(\Q(\sqrt{2305}) \) None \(-32\) \(-14\) \(-2730\) \(4802\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+(-7-5\beta )q^{3}+2^{8}q^{4}+(-1365+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(14)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)