Properties

Label 245.10.a
Level $245$
Weight $10$
Character orbit 245.a
Rep. character $\chi_{245}(1,\cdot)$
Character field $\Q$
Dimension $123$
Newform subspaces $15$
Sturm bound $280$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 245.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(280\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(245))\).

Total New Old
Modular forms 260 123 137
Cusp forms 244 123 121
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
\(+\)\(+\)\(+\)\(29\)
\(+\)\(-\)\(-\)\(33\)
\(-\)\(+\)\(-\)\(31\)
\(-\)\(-\)\(+\)\(30\)
Plus space\(+\)\(59\)
Minus space\(-\)\(64\)

Trace form

\( 123 q + 50 q^{2} + 146 q^{3} + 30976 q^{4} - 625 q^{5} + 120 q^{6} + 55332 q^{8} + 747647 q^{9} + O(q^{10}) \) \( 123 q + 50 q^{2} + 146 q^{3} + 30976 q^{4} - 625 q^{5} + 120 q^{6} + 55332 q^{8} + 747647 q^{9} - 21250 q^{10} - 66196 q^{11} + 199436 q^{12} - 93534 q^{13} - 31250 q^{15} + 7517236 q^{16} + 356990 q^{17} + 28958 q^{18} - 518568 q^{19} - 932500 q^{20} - 5260264 q^{22} + 5283346 q^{23} + 1570132 q^{24} + 48046875 q^{25} - 19131552 q^{26} + 1722308 q^{27} - 4108130 q^{29} + 855000 q^{30} + 12667708 q^{31} + 42764404 q^{32} - 46451880 q^{33} - 14559780 q^{34} + 128215896 q^{36} + 73439126 q^{37} + 14270500 q^{38} + 30064716 q^{39} - 32835000 q^{40} - 61003334 q^{41} - 107787142 q^{43} + 39890212 q^{44} - 39565625 q^{45} + 124732556 q^{46} - 28362334 q^{47} + 201892524 q^{48} + 19531250 q^{50} + 168701244 q^{51} - 88413024 q^{52} + 63368254 q^{53} + 118759324 q^{54} + 48335000 q^{55} + 486450704 q^{57} - 291910792 q^{58} + 130890704 q^{59} + 183702500 q^{60} + 315200674 q^{61} + 206213544 q^{62} + 1740196620 q^{64} - 73201250 q^{65} + 896660604 q^{66} + 325989198 q^{67} + 663170644 q^{68} - 439827468 q^{69} - 286870420 q^{71} - 1133150864 q^{72} - 370085770 q^{73} - 1334085264 q^{74} + 57031250 q^{75} + 1523192108 q^{76} + 1039087272 q^{78} + 732597960 q^{79} - 1336790000 q^{80} + 4424658199 q^{81} - 372376144 q^{82} - 1331291174 q^{83} + 689276250 q^{85} + 2620304736 q^{86} - 3282442652 q^{87} - 1109567152 q^{88} + 2769543798 q^{89} + 452386250 q^{90} - 44664676 q^{92} + 1352429664 q^{93} + 4915128468 q^{94} + 808802500 q^{95} - 599218692 q^{96} - 678170858 q^{97} + 485561676 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(245))\) 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
245.10.a.a 245.a 1.a $1$ $126.184$ \(\Q\) None 5.10.a.a \(-8\) \(114\) \(625\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-8q^{2}+114q^{3}-448q^{4}+5^{4}q^{5}+\cdots\)
245.10.a.b 245.a 1.a $1$ $126.184$ \(\Q\) None 35.10.a.a \(28\) \(116\) \(-625\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+28q^{2}+116q^{3}+272q^{4}-5^{4}q^{5}+\cdots\)
245.10.a.c 245.a 1.a $2$ $126.184$ \(\Q(\sqrt{2}) \) None 35.10.a.b \(-24\) \(174\) \(-1250\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-12+\beta )q^{2}+(87-54\beta )q^{3}+(-360+\cdots)q^{4}+\cdots\)
245.10.a.d 245.a 1.a $2$ $126.184$ \(\Q(\sqrt{1009}) \) None 5.10.a.b \(-10\) \(-260\) \(-1250\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-5-\beta )q^{2}+(-130-2\beta )q^{3}+(522+\cdots)q^{4}+\cdots\)
245.10.a.e 245.a 1.a $4$ $126.184$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 35.10.a.c \(-19\) \(18\) \(2500\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-5-\beta _{1})q^{2}+(4-\beta _{2})q^{3}+(435+\cdots)q^{4}+\cdots\)
245.10.a.f 245.a 1.a $5$ $126.184$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 35.10.a.d \(2\) \(-140\) \(3125\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-28-\beta _{2})q^{3}+(168-4\beta _{1}+\cdots)q^{4}+\cdots\)
245.10.a.g 245.a 1.a $6$ $126.184$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 35.10.a.e \(15\) \(124\) \(-3750\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(3-\beta _{1})q^{2}+(20+\beta _{1}-\beta _{2})q^{3}+(503+\cdots)q^{4}+\cdots\)
245.10.a.h 245.a 1.a $9$ $126.184$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 245.10.a.h \(1\) \(-268\) \(5625\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-30-\beta _{1}+\beta _{3})q^{3}+(208+\cdots)q^{4}+\cdots\)
245.10.a.i 245.a 1.a $9$ $126.184$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 245.10.a.h \(1\) \(268\) \(-5625\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(30+\beta _{1}-\beta _{3})q^{3}+(208+\cdots)q^{4}+\cdots\)
245.10.a.j 245.a 1.a $11$ $126.184$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None 35.10.e.a \(-33\) \(-56\) \(6875\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{1})q^{2}+(-5-\beta _{3})q^{3}+(250+\cdots)q^{4}+\cdots\)
245.10.a.k 245.a 1.a $11$ $126.184$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None 35.10.e.a \(-33\) \(56\) \(-6875\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{1})q^{2}+(5+\beta _{3})q^{3}+(250+\cdots)q^{4}+\cdots\)
245.10.a.l 245.a 1.a $13$ $126.184$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 35.10.e.b \(-1\) \(-268\) \(-8125\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-21-\beta _{3})q^{3}+(274+\beta _{1}+\cdots)q^{4}+\cdots\)
245.10.a.m 245.a 1.a $13$ $126.184$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 35.10.e.b \(-1\) \(268\) \(8125\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(21+\beta _{3})q^{3}+(274+\beta _{1}+\cdots)q^{4}+\cdots\)
245.10.a.n 245.a 1.a $18$ $126.184$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None 245.10.a.n \(66\) \(-112\) \(-11250\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(4-\beta _{1})q^{2}+(-6+\beta _{4})q^{3}+(249+\cdots)q^{4}+\cdots\)
245.10.a.o 245.a 1.a $18$ $126.184$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None 245.10.a.n \(66\) \(112\) \(11250\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(4-\beta _{1})q^{2}+(6-\beta _{4})q^{3}+(249-6\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(245))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(245)) \simeq \) \(S_{10}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)