Properties

Label 245.6.a
Level $245$
Weight $6$
Character orbit 245.a
Rep. character $\chi_{245}(1,\cdot)$
Character field $\Q$
Dimension $69$
Newform subspaces $13$
Sturm bound $168$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 245.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(168\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(245))\).

Total New Old
Modular forms 148 69 79
Cusp forms 132 69 63
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.

\(5\)\(7\)FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
\(+\)\(+\)\(+\)\(34\)\(16\)\(18\)\(30\)\(16\)\(14\)\(4\)\(0\)\(4\)
\(+\)\(-\)\(-\)\(39\)\(19\)\(20\)\(35\)\(19\)\(16\)\(4\)\(0\)\(4\)
\(-\)\(+\)\(-\)\(38\)\(18\)\(20\)\(34\)\(18\)\(16\)\(4\)\(0\)\(4\)
\(-\)\(-\)\(+\)\(37\)\(16\)\(21\)\(33\)\(16\)\(17\)\(4\)\(0\)\(4\)
Plus space\(+\)\(71\)\(32\)\(39\)\(63\)\(32\)\(31\)\(8\)\(0\)\(8\)
Minus space\(-\)\(77\)\(37\)\(40\)\(69\)\(37\)\(32\)\(8\)\(0\)\(8\)

Trace form

\( 69 q + 6 q^{2} - 40 q^{3} + 1168 q^{4} - 25 q^{5} + 72 q^{6} - 348 q^{8} + 5765 q^{9} - 150 q^{10} + 1420 q^{11} - 3796 q^{12} - 690 q^{13} + 1000 q^{15} + 19124 q^{16} - 1822 q^{17} + 7202 q^{18} - 1916 q^{19}+ \cdots + 1230636 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(245))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 7
245.6.a.a 245.a 1.a $1$ $39.294$ \(\Q\) None 35.6.a.a \(-8\) \(-1\) \(-25\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-8q^{2}-q^{3}+2^{5}q^{4}-5^{2}q^{5}+8q^{6}+\cdots\)
245.6.a.b 245.a 1.a $1$ $39.294$ \(\Q\) None 5.6.a.a \(2\) \(4\) \(-25\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{3}-28q^{4}-5^{2}q^{5}+8q^{6}+\cdots\)
245.6.a.c 245.a 1.a $2$ $39.294$ \(\Q(\sqrt{65}) \) None 35.6.a.b \(1\) \(-3\) \(50\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-3+3\beta )q^{3}+(-2^{4}+\beta )q^{4}+\cdots\)
245.6.a.d 245.a 1.a $3$ $39.294$ 3.3.577880.1 None 35.6.a.c \(-6\) \(-26\) \(75\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(-9-\beta _{2})q^{3}+(38+\cdots)q^{4}+\cdots\)
245.6.a.e 245.a 1.a $4$ $39.294$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 35.6.a.d \(7\) \(-14\) \(-100\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}+(-4+\beta _{1}-\beta _{3})q^{3}+\cdots\)
245.6.a.f 245.a 1.a $5$ $39.294$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 245.6.a.f \(-3\) \(-7\) \(125\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
245.6.a.g 245.a 1.a $5$ $39.294$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 245.6.a.f \(-3\) \(7\) \(-125\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
245.6.a.h 245.a 1.a $6$ $39.294$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 35.6.e.a \(-5\) \(-20\) \(150\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-3-\beta _{1}+\beta _{3})q^{3}+\cdots\)
245.6.a.i 245.a 1.a $6$ $39.294$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 35.6.e.a \(-5\) \(20\) \(-150\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(3+\beta _{1}-\beta _{3})q^{3}+\cdots\)
245.6.a.j 245.a 1.a $8$ $39.294$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 35.6.e.b \(3\) \(-2\) \(200\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(5^{2}+\beta _{1}+\beta _{2})q^{4}+\cdots\)
245.6.a.k 245.a 1.a $8$ $39.294$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 35.6.e.b \(3\) \(2\) \(-200\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(5^{2}+\beta _{1}+\beta _{2})q^{4}+\cdots\)
245.6.a.l 245.a 1.a $10$ $39.294$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 245.6.a.l \(10\) \(-58\) \(-250\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-6+\beta _{3})q^{3}+(18-\beta _{1}+\cdots)q^{4}+\cdots\)
245.6.a.m 245.a 1.a $10$ $39.294$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 245.6.a.l \(10\) \(58\) \(250\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(6-\beta _{3})q^{3}+(18-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(245))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(245)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)