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.

\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(16\)
\(+\)\(-\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(18\)
\(-\)\(-\)\(+\)\(16\)
Plus space\(+\)\(32\)
Minus space\(-\)\(37\)

Trace form

\( 69 q + 6 q^{2} - 40 q^{3} + 1168 q^{4} - 25 q^{5} + 72 q^{6} - 348 q^{8} + 5765 q^{9} + O(q^{10}) \) \( 69 q + 6 q^{2} - 40 q^{3} + 1168 q^{4} - 25 q^{5} + 72 q^{6} - 348 q^{8} + 5765 q^{9} - 150 q^{10} + 1420 q^{11} - 3796 q^{12} - 690 q^{13} + 1000 q^{15} + 19124 q^{16} - 1822 q^{17} + 7202 q^{18} - 1916 q^{19} + 700 q^{20} - 1560 q^{22} + 1436 q^{23} + 15124 q^{24} + 43125 q^{25} + 8808 q^{26} - 1732 q^{27} + 994 q^{29} - 7800 q^{30} - 1692 q^{31} + 500 q^{32} + 26628 q^{33} + 23364 q^{34} + 94824 q^{36} + 30054 q^{37} - 700 q^{38} - 50040 q^{39} - 12600 q^{40} - 14246 q^{41} - 31096 q^{43} - 15132 q^{44} - 125 q^{45} + 17468 q^{46} - 35116 q^{47} - 13332 q^{48} + 3750 q^{50} + 10056 q^{51} - 11776 q^{52} - 8634 q^{53} + 21628 q^{54} - 24100 q^{55} - 108112 q^{57} - 45776 q^{58} - 67192 q^{59} + 80900 q^{60} - 7230 q^{61} + 97320 q^{62} + 238988 q^{64} + 26550 q^{65} + 108732 q^{66} - 66040 q^{67} - 37900 q^{68} - 129780 q^{69} + 40200 q^{71} + 95728 q^{72} + 88014 q^{73} - 114536 q^{74} - 25000 q^{75} + 101676 q^{76} + 146472 q^{78} - 118008 q^{79} + 48400 q^{80} + 280549 q^{81} - 360968 q^{82} + 105540 q^{83} - 61550 q^{85} + 227696 q^{86} + 241348 q^{87} - 47344 q^{88} + 306526 q^{89} - 163450 q^{90} + 65020 q^{92} + 155112 q^{93} - 309980 q^{94} + 82100 q^{95} + 256188 q^{96} - 72870 q^{97} + 1230636 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 7
245.6.a.a \(1\) \(39.294\) \(\Q\) None \(-8\) \(-1\) \(-25\) \(0\) \(+\) \(-\) \(q-8q^{2}-q^{3}+2^{5}q^{4}-5^{2}q^{5}+8q^{6}+\cdots\)
245.6.a.b \(1\) \(39.294\) \(\Q\) None \(2\) \(4\) \(-25\) \(0\) \(+\) \(-\) \(q+2q^{2}+4q^{3}-28q^{4}-5^{2}q^{5}+8q^{6}+\cdots\)
245.6.a.c \(2\) \(39.294\) \(\Q(\sqrt{65}) \) None \(1\) \(-3\) \(50\) \(0\) \(-\) \(-\) \(q+\beta q^{2}+(-3+3\beta )q^{3}+(-2^{4}+\beta )q^{4}+\cdots\)
245.6.a.d \(3\) \(39.294\) 3.3.577880.1 None \(-6\) \(-26\) \(75\) \(0\) \(-\) \(-\) \(q+(-2+\beta _{1})q^{2}+(-9-\beta _{2})q^{3}+(38+\cdots)q^{4}+\cdots\)
245.6.a.e \(4\) \(39.294\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(7\) \(-14\) \(-100\) \(0\) \(+\) \(-\) \(q+(2-\beta _{1})q^{2}+(-4+\beta _{1}-\beta _{3})q^{3}+\cdots\)
245.6.a.f \(5\) \(39.294\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-3\) \(-7\) \(125\) \(0\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
245.6.a.g \(5\) \(39.294\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-3\) \(7\) \(-125\) \(0\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
245.6.a.h \(6\) \(39.294\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-5\) \(-20\) \(150\) \(0\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-3-\beta _{1}+\beta _{3})q^{3}+\cdots\)
245.6.a.i \(6\) \(39.294\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-5\) \(20\) \(-150\) \(0\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}+(3+\beta _{1}-\beta _{3})q^{3}+\cdots\)
245.6.a.j \(8\) \(39.294\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(3\) \(-2\) \(200\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(5^{2}+\beta _{1}+\beta _{2})q^{4}+\cdots\)
245.6.a.k \(8\) \(39.294\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(3\) \(2\) \(-200\) \(0\) \(+\) \(-\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(5^{2}+\beta _{1}+\beta _{2})q^{4}+\cdots\)
245.6.a.l \(10\) \(39.294\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(-58\) \(-250\) \(0\) \(+\) \(+\) \(q+(1-\beta _{1})q^{2}+(-6+\beta _{3})q^{3}+(18-\beta _{1}+\cdots)q^{4}+\cdots\)
245.6.a.m \(10\) \(39.294\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(58\) \(250\) \(0\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(6-\beta _{3})q^{3}+(18-\beta _{1}+\cdots)q^{4}+\cdots\)

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

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