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Properties

Label 245.4.a
Level $245$
Weight $4$
Character orbit 245.a
Rep. character $\chi_{245}(1,\cdot)$
Character field $\Q$
Dimension $41$
Newform subspaces $16$
Sturm bound $112$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(112\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(245))\).

Total New Old
Modular forms 92 41 51
Cusp forms 76 41 35
Eisenstein series 16 0 16

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

\(5\)\(7\)FrickeDim
\(+\)\(+\)$+$\(11\)
\(+\)\(-\)$-$\(9\)
\(-\)\(+\)$-$\(9\)
\(-\)\(-\)$+$\(12\)
Plus space\(+\)\(23\)
Minus space\(-\)\(18\)

Trace form

\( 41 q + 2 q^{3} + 148 q^{4} + 5 q^{5} - 36 q^{8} + 341 q^{9} + O(q^{10}) \) \( 41 q + 2 q^{3} + 148 q^{4} + 5 q^{5} - 36 q^{8} + 341 q^{9} + 40 q^{10} + 28 q^{11} + 188 q^{12} + 22 q^{13} - 50 q^{15} + 772 q^{16} + 170 q^{17} + 356 q^{18} - 344 q^{19} + 40 q^{20} - 32 q^{22} - 238 q^{23} - 44 q^{24} + 1025 q^{25} + 156 q^{26} - 76 q^{27} - 110 q^{29} - 240 q^{30} + 156 q^{31} - 1228 q^{32} - 360 q^{33} - 360 q^{34} + 1932 q^{36} - 1342 q^{37} + 500 q^{38} - 372 q^{39} + 240 q^{40} - 458 q^{41} - 694 q^{43} + 996 q^{44} - 275 q^{45} - 1148 q^{46} + 1058 q^{47} + 2028 q^{48} + 1308 q^{51} - 2072 q^{52} - 102 q^{53} - 788 q^{54} + 520 q^{55} + 2672 q^{57} - 2084 q^{58} + 1472 q^{59} + 260 q^{60} - 762 q^{61} + 552 q^{62} + 2540 q^{64} - 870 q^{65} - 1092 q^{66} + 2254 q^{67} - 2692 q^{68} - 204 q^{69} - 180 q^{71} + 1768 q^{72} - 190 q^{73} + 508 q^{74} + 50 q^{75} - 4084 q^{76} - 2136 q^{78} + 3880 q^{79} + 1120 q^{80} + 3733 q^{81} + 508 q^{82} + 2202 q^{83} + 30 q^{85} - 4408 q^{86} + 1684 q^{87} - 4784 q^{88} + 994 q^{89} + 2780 q^{90} - 6548 q^{92} - 2352 q^{93} + 444 q^{94} + 20 q^{95} + 6396 q^{96} - 4254 q^{97} - 7332 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(245))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 7
245.4.a.a 245.a 1.a $1$ $14.455$ \(\Q\) None \(-4\) \(-2\) \(5\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-2q^{3}+8q^{4}+5q^{5}+8q^{6}+\cdots\)
245.4.a.b 245.a 1.a $1$ $14.455$ \(\Q\) None \(1\) \(-6\) \(5\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-6q^{3}-7q^{4}+5q^{5}-6q^{6}+\cdots\)
245.4.a.c 245.a 1.a $1$ $14.455$ \(\Q\) None \(1\) \(6\) \(-5\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+6q^{3}-7q^{4}-5q^{5}+6q^{6}+\cdots\)
245.4.a.d 245.a 1.a $1$ $14.455$ \(\Q\) None \(1\) \(8\) \(5\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+8q^{3}-7q^{4}+5q^{5}+8q^{6}+\cdots\)
245.4.a.e 245.a 1.a $1$ $14.455$ \(\Q\) None \(3\) \(-2\) \(5\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{2}-2q^{3}+q^{4}+5q^{5}-6q^{6}+\cdots\)
245.4.a.f 245.a 1.a $1$ $14.455$ \(\Q\) None \(3\) \(2\) \(-5\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{2}+2q^{3}+q^{4}-5q^{5}+6q^{6}+\cdots\)
245.4.a.g 245.a 1.a $2$ $14.455$ \(\Q(\sqrt{2}) \) None \(-6\) \(-2\) \(10\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-3+\beta )q^{2}+(-1-3\beta )q^{3}+(3-6\beta )q^{4}+\cdots\)
245.4.a.h 245.a 1.a $2$ $14.455$ \(\Q(\sqrt{2}) \) None \(-6\) \(2\) \(-10\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-3+\beta )q^{2}+(1+3\beta )q^{3}+(3-6\beta )q^{4}+\cdots\)
245.4.a.i 245.a 1.a $2$ $14.455$ \(\Q(\sqrt{11}) \) None \(2\) \(-10\) \(-10\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-5q^{3}+(4+2\beta )q^{4}-5q^{5}+\cdots\)
245.4.a.j 245.a 1.a $2$ $14.455$ \(\Q(\sqrt{11}) \) None \(2\) \(10\) \(10\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+5q^{3}+(4+2\beta )q^{4}+5q^{5}+\cdots\)
245.4.a.k 245.a 1.a $2$ $14.455$ \(\Q(\sqrt{2}) \) None \(8\) \(-2\) \(10\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(4+\beta )q^{2}+(-1+4\beta )q^{3}+(10+8\beta )q^{4}+\cdots\)
245.4.a.l 245.a 1.a $3$ $14.455$ 3.3.14360.1 None \(-3\) \(-2\) \(-15\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}+\beta _{2})q^{3}+\cdots\)
245.4.a.m 245.a 1.a $5$ $14.455$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(1\) \(-8\) \(-25\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{3}+(7+\beta _{3})q^{4}+\cdots\)
245.4.a.n 245.a 1.a $5$ $14.455$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(1\) \(8\) \(25\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2-\beta _{2})q^{3}+(7+\beta _{3})q^{4}+\cdots\)
245.4.a.o 245.a 1.a $6$ $14.455$ 6.6.1163891200.1 None \(-2\) \(-16\) \(30\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-3+\beta _{5})q^{3}+(2+3\beta _{1}+\cdots)q^{4}+\cdots\)
245.4.a.p 245.a 1.a $6$ $14.455$ 6.6.1163891200.1 None \(-2\) \(16\) \(-30\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(3-\beta _{5})q^{3}+(2+3\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(245))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(245)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)