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Properties

Label 245.4.e
Level $245$
Weight $4$
Character orbit 245.e
Rep. character $\chi_{245}(116,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $17$
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 17 \)
Sturm bound: \(112\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(245, [\chi])\).

Total New Old
Modular forms 184 80 104
Cusp forms 152 80 72
Eisenstein series 32 0 32

Trace form

\( 80 q - 4 q^{2} - 12 q^{3} - 140 q^{4} - 10 q^{5} - 8 q^{6} - 72 q^{8} - 406 q^{9} + O(q^{10}) \) \( 80 q - 4 q^{2} - 12 q^{3} - 140 q^{4} - 10 q^{5} - 8 q^{6} - 72 q^{8} - 406 q^{9} - 20 q^{10} + 46 q^{11} - 34 q^{12} - 48 q^{13} - 80 q^{15} - 752 q^{16} - 132 q^{17} - 138 q^{18} + 18 q^{19} + 280 q^{20} - 984 q^{22} + 412 q^{23} + 728 q^{24} - 1000 q^{25} + 278 q^{26} + 840 q^{27} + 636 q^{29} - 140 q^{30} + 168 q^{31} + 224 q^{32} - 320 q^{33} - 824 q^{34} + 1040 q^{36} + 180 q^{37} + 96 q^{38} + 632 q^{39} - 240 q^{40} + 384 q^{41} - 424 q^{43} + 1150 q^{44} - 600 q^{45} + 578 q^{46} - 624 q^{47} - 164 q^{48} + 200 q^{50} + 88 q^{51} - 668 q^{52} + 20 q^{53} - 72 q^{54} + 640 q^{55} + 408 q^{57} + 3334 q^{58} + 1188 q^{59} + 1130 q^{60} + 2434 q^{61} - 360 q^{62} + 7784 q^{64} + 430 q^{65} + 1988 q^{66} - 2716 q^{67} - 4696 q^{68} - 3324 q^{69} - 6224 q^{71} - 2650 q^{72} - 1156 q^{73} - 3798 q^{74} - 300 q^{75} - 852 q^{76} + 15280 q^{78} - 3700 q^{79} - 1280 q^{80} - 5412 q^{81} + 2050 q^{82} + 5280 q^{83} + 2000 q^{85} + 3144 q^{86} + 1684 q^{87} + 13352 q^{88} + 1778 q^{89} - 540 q^{90} - 13780 q^{92} - 4332 q^{93} - 2210 q^{94} + 320 q^{95} + 6404 q^{96} - 1744 q^{97} - 22516 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(245, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
245.4.e.a 245.e 7.c $2$ $14.455$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-2\) \(5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-3\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
245.4.e.b 245.e 7.c $2$ $14.455$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-8\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-8+8\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
245.4.e.c 245.e 7.c $2$ $14.455$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-6\) \(5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-6+6\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
245.4.e.d 245.e 7.c $2$ $14.455$ \(\Q(\sqrt{-3}) \) None \(-1\) \(6\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(6-6\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
245.4.e.e 245.e 7.c $2$ $14.455$ \(\Q(\sqrt{-3}) \) None \(-1\) \(8\) \(5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(8-8\zeta_{6})q^{3}+(7-7\zeta_{6})q^{4}+\cdots\)
245.4.e.f 245.e 7.c $2$ $14.455$ \(\Q(\sqrt{-3}) \) None \(4\) \(-2\) \(5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
245.4.e.g 245.e 7.c $2$ $14.455$ \(\Q(\sqrt{-3}) \) None \(4\) \(2\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+4\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-8+8\zeta_{6})q^{4}+\cdots\)
245.4.e.h 245.e 7.c $4$ $14.455$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-8\) \(-2\) \(10\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+4\beta _{2}-\beta _{3})q^{2}+(-1-4\beta _{1}+\cdots)q^{3}+\cdots\)
245.4.e.i 245.e 7.c $4$ $14.455$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-8\) \(2\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+4\beta _{2}-\beta _{3})q^{2}+(1+4\beta _{1}+\cdots)q^{3}+\cdots\)
245.4.e.j 245.e 7.c $4$ $14.455$ \(\Q(\sqrt{-3}, \sqrt{11})\) None \(-2\) \(-10\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+5\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
245.4.e.k 245.e 7.c $4$ $14.455$ \(\Q(\sqrt{-3}, \sqrt{11})\) None \(-2\) \(10\) \(10\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}-5\beta _{2}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)
245.4.e.l 245.e 7.c $4$ $14.455$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(6\) \(-2\) \(10\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-3\beta _{2}+\beta _{3})q^{2}+(-1-3\beta _{1}+\cdots)q^{3}+\cdots\)
245.4.e.m 245.e 7.c $6$ $14.455$ 6.0.5567659200.1 None \(3\) \(-2\) \(-15\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}-\beta _{2}-\beta _{3})q^{2}+(\beta _{1}-\beta _{3}+\cdots)q^{3}+\cdots\)
245.4.e.n 245.e 7.c $6$ $14.455$ 6.0.5567659200.1 None \(3\) \(2\) \(15\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}-\beta _{2}-\beta _{3})q^{2}+(-\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
245.4.e.o 245.e 7.c $10$ $14.455$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-1\) \(-8\) \(-25\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{2})q^{2}+(-\beta _{3}-\beta _{5}-2\beta _{7}+\cdots)q^{3}+\cdots\)
245.4.e.p 245.e 7.c $12$ $14.455$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(-16\) \(30\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{2}+(-3-3\beta _{3}+\beta _{7}+\beta _{9})q^{3}+\cdots\)
245.4.e.q 245.e 7.c $12$ $14.455$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(16\) \(-30\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{5}q^{2}+(3+3\beta _{3}-\beta _{7}-\beta _{9})q^{3}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(245, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)