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Properties

Label 29.12.a
Level $29$
Weight $12$
Character orbit 29.a
Rep. character $\chi_{29}(1,\cdot)$
Character field $\Q$
Dimension $25$
Newform subspaces $2$
Sturm bound $30$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(30\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(29))\).

Total New Old
Modular forms 29 25 4
Cusp forms 27 25 2
Eisenstein series 2 0 2

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

\(29\)Dim
\(+\)\(14\)
\(-\)\(11\)

Trace form

\( 25 q - 32 q^{2} - 506 q^{3} + 27508 q^{4} + 7020 q^{5} - 9748 q^{6} + 35592 q^{7} - 23466 q^{8} + 1702895 q^{9} + O(q^{10}) \) \( 25 q - 32 q^{2} - 506 q^{3} + 27508 q^{4} + 7020 q^{5} - 9748 q^{6} + 35592 q^{7} - 23466 q^{8} + 1702895 q^{9} + 27742 q^{10} - 214226 q^{11} - 1448262 q^{12} + 3782804 q^{13} - 3244312 q^{14} - 7226682 q^{15} + 22039956 q^{16} + 2332410 q^{17} - 28089770 q^{18} - 14318088 q^{19} + 15688344 q^{20} + 4311032 q^{21} + 123898648 q^{22} - 36029772 q^{23} - 3185836 q^{24} + 150774941 q^{25} + 48581774 q^{26} + 161043970 q^{27} - 71773076 q^{28} - 61533447 q^{29} - 71896156 q^{30} + 341805414 q^{31} + 627748370 q^{32} + 101067010 q^{33} + 202797124 q^{34} + 287033648 q^{35} + 961349640 q^{36} - 891764134 q^{37} + 669987788 q^{38} + 785688014 q^{39} - 886667226 q^{40} - 863852330 q^{41} + 1216983428 q^{42} + 2267776694 q^{43} + 79414186 q^{44} + 3398674874 q^{45} - 1655195592 q^{46} - 5997173870 q^{47} - 12916902578 q^{48} + 5797744465 q^{49} + 2863677314 q^{50} + 12065621100 q^{51} - 1290671508 q^{52} - 5404446152 q^{53} + 8456593504 q^{54} - 2917362106 q^{55} - 16274680360 q^{56} - 8981654972 q^{57} - 656356768 q^{58} + 1582222352 q^{59} - 4208701494 q^{60} - 26261200706 q^{61} + 12051817568 q^{62} - 33002113192 q^{63} + 26534985848 q^{64} + 33398592218 q^{65} - 56828053010 q^{66} + 49262818932 q^{67} - 74589188368 q^{68} - 35166714476 q^{69} - 25086206272 q^{70} - 25920455684 q^{71} + 22998940072 q^{72} - 18078498554 q^{73} + 25865342492 q^{74} + 58300418044 q^{75} + 133599439548 q^{76} + 39645526984 q^{77} + 38864633664 q^{78} - 14679807442 q^{79} + 61922455276 q^{80} + 121701036885 q^{81} - 64150349656 q^{82} - 14617919800 q^{83} + 81165635120 q^{84} - 97745332000 q^{85} - 55291873840 q^{86} - 29905255242 q^{87} + 237645067640 q^{88} + 91125382134 q^{89} + 70813178716 q^{90} - 296771641312 q^{91} - 282075353192 q^{92} + 222059520878 q^{93} + 290303285012 q^{94} - 125987091284 q^{95} + 238924679544 q^{96} - 165904914514 q^{97} - 608672866304 q^{98} + 96294484764 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(29))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 29
29.12.a.a 29.a 1.a $11$ $22.282$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None 29.12.a.a \(-32\) \(-982\) \(-2740\) \(-49432\) $-$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{1})q^{2}+(-89-\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
29.12.a.b 29.a 1.a $14$ $22.282$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 29.12.a.b \(0\) \(476\) \(9760\) \(85024\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(34-\beta _{3})q^{3}+(1312+3\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(29))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(29)) \simeq \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)