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Properties

Label 14.12.a
Level $14$
Weight $12$
Character orbit 14.a
Rep. character $\chi_{14}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $24$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 14.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(24\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(14))\).

Total New Old
Modular forms 24 6 18
Cusp forms 20 6 14
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
\(+\)\(+\)$+$\(2\)
\(+\)\(-\)$-$\(1\)
\(-\)\(+\)$-$\(1\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(2\)

Trace form

\( 6 q - 486 q^{3} + 6144 q^{4} + 3874 q^{5} - 12608 q^{6} + 236810 q^{9} + O(q^{10}) \) \( 6 q - 486 q^{3} + 6144 q^{4} + 3874 q^{5} - 12608 q^{6} + 236810 q^{9} - 363456 q^{10} + 1323884 q^{11} - 497664 q^{12} + 2203470 q^{13} + 1075648 q^{14} + 5705912 q^{15} + 6291456 q^{16} - 1696024 q^{17} + 8028288 q^{18} + 1371822 q^{19} + 3966976 q^{20} - 16907842 q^{21} - 177792 q^{22} + 51566600 q^{23} - 12910592 q^{24} - 34525650 q^{25} - 98434880 q^{26} - 100431252 q^{27} - 97880648 q^{29} - 45829888 q^{30} + 204823500 q^{31} - 890574080 q^{33} - 63911808 q^{34} + 307601714 q^{35} + 242493440 q^{36} + 110267784 q^{37} + 415977024 q^{38} + 2580022976 q^{39} - 372178944 q^{40} - 1161081216 q^{41} + 261382464 q^{42} - 712891884 q^{43} + 1355657216 q^{44} + 3398855098 q^{45} + 722366208 q^{46} - 6223597068 q^{47} - 509607936 q^{48} + 1694851494 q^{49} - 3835608704 q^{50} + 6795792268 q^{51} + 2256353280 q^{52} + 7496822532 q^{53} - 11261453696 q^{54} - 7139455944 q^{55} + 1101463552 q^{56} - 17118924588 q^{57} + 9231563136 q^{58} - 20944130 q^{59} + 5842853888 q^{60} - 31239227502 q^{61} + 731196544 q^{62} + 9215547012 q^{63} + 6442450944 q^{64} + 14130637836 q^{65} - 12745084928 q^{66} + 17160124848 q^{67} - 1736728576 q^{68} + 15450049648 q^{69} + 2223364416 q^{70} - 13278746440 q^{71} + 8220966912 q^{72} + 51888151572 q^{73} - 14296955520 q^{74} + 28242983150 q^{75} + 1404745728 q^{76} + 6150622492 q^{77} - 13353795584 q^{78} - 42429894648 q^{79} + 4062183424 q^{80} + 8086601882 q^{81} + 35503508352 q^{82} - 47165805994 q^{83} - 17313630208 q^{84} + 22723837572 q^{85} + 27251479680 q^{86} - 82159329436 q^{87} - 182059008 q^{88} + 116340860076 q^{89} - 25887488192 q^{90} - 65994332586 q^{91} + 52804198400 q^{92} - 254334974536 q^{93} - 50402446464 q^{94} - 239833928104 q^{95} - 13220446208 q^{96} + 217462992744 q^{97} + 281841334172 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(14))\) 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
14.12.a.a 14.a 1.a $1$ $10.757$ \(\Q\) None \(-32\) \(-396\) \(7350\) \(16807\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}-396q^{3}+2^{10}q^{4}+7350q^{5}+\cdots\)
14.12.a.b 14.a 1.a $1$ $10.757$ \(\Q\) None \(32\) \(-90\) \(-7480\) \(-16807\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}-90q^{3}+2^{10}q^{4}-7480q^{5}+\cdots\)
14.12.a.c 14.a 1.a $2$ $10.757$ \(\Q(\sqrt{153169}) \) None \(-64\) \(350\) \(266\) \(-33614\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}+(175-\beta )q^{3}+2^{10}q^{4}+(133+\cdots)q^{5}+\cdots\)
14.12.a.d 14.a 1.a $2$ $10.757$ \(\Q(\sqrt{352969}) \) None \(64\) \(-350\) \(3738\) \(33614\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}+(-175-\beta )q^{3}+2^{10}q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(14)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)