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Properties

Label 12.10.a
Level $12$
Weight $10$
Character orbit 12.a
Rep. character $\chi_{12}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 12.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(12))\).

Total New Old
Modular forms 21 1 20
Cusp forms 15 1 14
Eisenstein series 6 0 6

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

\(2\)\(3\)FrickeDim
\(-\)\(+\)$-$\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q - 81 q^{3} + 990 q^{5} + 8576 q^{7} + 6561 q^{9} + O(q^{10}) \) \( q - 81 q^{3} + 990 q^{5} + 8576 q^{7} + 6561 q^{9} + 70596 q^{11} - 2530 q^{13} - 80190 q^{15} - 200574 q^{17} - 695620 q^{19} - 694656 q^{21} + 2472696 q^{23} - 973025 q^{25} - 531441 q^{27} + 5474214 q^{29} + 3732104 q^{31} - 5718276 q^{33} + 8490240 q^{35} - 21898522 q^{37} + 204930 q^{39} - 23818950 q^{41} + 10612676 q^{43} + 6495390 q^{45} + 2398464 q^{47} + 33194169 q^{49} + 16246494 q^{51} - 8994978 q^{53} + 69890040 q^{55} + 56345220 q^{57} - 143417916 q^{59} - 19804258 q^{61} + 56267136 q^{63} - 2504700 q^{65} - 165625156 q^{67} - 200288376 q^{69} - 194801400 q^{71} + 148729418 q^{73} + 78815025 q^{75} + 605431296 q^{77} - 30134152 q^{79} + 43046721 q^{81} + 302054076 q^{83} - 198568260 q^{85} - 443411334 q^{87} + 909502650 q^{89} - 21697280 q^{91} - 302300424 q^{93} - 688663800 q^{95} - 872463358 q^{97} + 463180356 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(12))\) 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 3
12.10.a.a 12.a 1.a $1$ $6.180$ \(\Q\) None \(0\) \(-81\) \(990\) \(8576\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3^{4}q^{3}+990q^{5}+8576q^{7}+3^{8}q^{9}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(12))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(12)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)