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Properties

Label 294.4.a
Level $294$
Weight $4$
Character orbit 294.a
Rep. character $\chi_{294}(1,\cdot)$
Character field $\Q$
Dimension $21$
Newform subspaces $15$
Sturm bound $224$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(224\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(294))\).

Total New Old
Modular forms 184 21 163
Cusp forms 152 21 131
Eisenstein series 32 0 32

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

\(2\)\(3\)\(7\)FrickeDim
\(+\)\(+\)\(+\)$+$\(3\)
\(+\)\(+\)\(-\)$-$\(2\)
\(+\)\(-\)\(+\)$-$\(3\)
\(+\)\(-\)\(-\)$+$\(3\)
\(-\)\(+\)\(+\)$-$\(2\)
\(-\)\(+\)\(-\)$+$\(3\)
\(-\)\(-\)\(+\)$+$\(4\)
\(-\)\(-\)\(-\)$-$\(1\)
Plus space\(+\)\(13\)
Minus space\(-\)\(8\)

Trace form

\( 21 q - 2 q^{2} + 3 q^{3} + 84 q^{4} - 26 q^{5} - 6 q^{6} - 8 q^{8} + 189 q^{9} + O(q^{10}) \) \( 21 q - 2 q^{2} + 3 q^{3} + 84 q^{4} - 26 q^{5} - 6 q^{6} - 8 q^{8} + 189 q^{9} - 28 q^{10} + 68 q^{11} + 12 q^{12} + 38 q^{13} + 66 q^{15} + 336 q^{16} + 122 q^{17} - 18 q^{18} + 12 q^{19} - 104 q^{20} + 112 q^{22} - 240 q^{23} - 24 q^{24} + 447 q^{25} + 228 q^{26} + 27 q^{27} - 202 q^{29} + 84 q^{30} + 104 q^{31} - 32 q^{32} - 156 q^{33} - 260 q^{34} + 756 q^{36} + 498 q^{37} + 104 q^{38} + 978 q^{39} - 112 q^{40} - 510 q^{41} + 328 q^{43} + 272 q^{44} - 234 q^{45} + 640 q^{46} + 192 q^{47} + 48 q^{48} + 1506 q^{50} - 414 q^{51} + 152 q^{52} + 1334 q^{53} - 54 q^{54} + 1240 q^{55} + 384 q^{57} + 684 q^{58} + 1924 q^{59} + 264 q^{60} + 758 q^{61} - 144 q^{62} + 1344 q^{64} + 316 q^{65} - 456 q^{66} - 2304 q^{67} + 488 q^{68} - 264 q^{69} - 1864 q^{71} - 72 q^{72} - 1646 q^{73} - 1724 q^{74} + 693 q^{75} + 48 q^{76} + 84 q^{78} - 1784 q^{79} - 416 q^{80} + 1701 q^{81} - 852 q^{82} - 772 q^{83} - 1412 q^{85} - 1032 q^{86} - 1014 q^{87} + 448 q^{88} - 1230 q^{89} - 252 q^{90} - 960 q^{92} - 3804 q^{93} - 152 q^{95} - 96 q^{96} + 106 q^{97} + 612 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(294))\) 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 7
294.4.a.a 294.a 1.a $1$ $17.347$ \(\Q\) None \(-2\) \(-3\) \(-15\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-15q^{5}+6q^{6}+\cdots\)
294.4.a.b 294.a 1.a $1$ $17.347$ \(\Q\) None \(-2\) \(-3\) \(-8\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-8q^{5}+6q^{6}+\cdots\)
294.4.a.c 294.a 1.a $1$ $17.347$ \(\Q\) None \(-2\) \(-3\) \(6\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots\)
294.4.a.d 294.a 1.a $1$ $17.347$ \(\Q\) None \(-2\) \(3\) \(-6\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{5}-6q^{6}+\cdots\)
294.4.a.e 294.a 1.a $1$ $17.347$ \(\Q\) None \(-2\) \(3\) \(-6\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-6q^{5}-6q^{6}+\cdots\)
294.4.a.f 294.a 1.a $1$ $17.347$ \(\Q\) None \(-2\) \(3\) \(8\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+8q^{5}-6q^{6}+\cdots\)
294.4.a.g 294.a 1.a $1$ $17.347$ \(\Q\) None \(-2\) \(3\) \(15\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+15q^{5}-6q^{6}+\cdots\)
294.4.a.h 294.a 1.a $1$ $17.347$ \(\Q\) None \(2\) \(-3\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\)
294.4.a.i 294.a 1.a $1$ $17.347$ \(\Q\) None \(2\) \(3\) \(-18\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}-18q^{5}+6q^{6}+\cdots\)
294.4.a.j 294.a 1.a $2$ $17.347$ \(\Q(\sqrt{2}) \) None \(-4\) \(-6\) \(12\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+(6+\beta )q^{5}+6q^{6}+\cdots\)
294.4.a.k 294.a 1.a $2$ $17.347$ \(\Q(\sqrt{2}) \) None \(-4\) \(6\) \(-12\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(-6+\beta )q^{5}+\cdots\)
294.4.a.l 294.a 1.a $2$ $17.347$ \(\Q(\sqrt{2}) \) None \(4\) \(-6\) \(-12\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(-6+\beta )q^{5}+\cdots\)
294.4.a.m 294.a 1.a $2$ $17.347$ \(\Q(\sqrt{1345}) \) None \(4\) \(-6\) \(-5\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(-2-\beta )q^{5}+\cdots\)
294.4.a.n 294.a 1.a $2$ $17.347$ \(\Q(\sqrt{1345}) \) None \(4\) \(6\) \(5\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(3-\beta )q^{5}+6q^{6}+\cdots\)
294.4.a.o 294.a 1.a $2$ $17.347$ \(\Q(\sqrt{2}) \) None \(4\) \(6\) \(12\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(6+\beta )q^{5}+6q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(294))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(294)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 2}\)