Properties

Label 605.6.a
Level $605$
Weight $6$
Character orbit 605.a
Rep. character $\chi_{605}(1,\cdot)$
Character field $\Q$
Dimension $181$
Newform subspaces $17$
Sturm bound $396$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 605.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(396\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(605))\).

Total New Old
Modular forms 342 181 161
Cusp forms 318 181 137
Eisenstein series 24 0 24

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

\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(42\)
\(+\)\(-\)\(-\)\(48\)
\(-\)\(+\)\(-\)\(48\)
\(-\)\(-\)\(+\)\(43\)
Plus space\(+\)\(85\)
Minus space\(-\)\(96\)

Trace form

\( 181 q - 2 q^{2} + 40 q^{3} + 2896 q^{4} + 25 q^{5} - 24 q^{6} - 4 q^{7} - 732 q^{8} + 14265 q^{9} + O(q^{10}) \) \( 181 q - 2 q^{2} + 40 q^{3} + 2896 q^{4} + 25 q^{5} - 24 q^{6} - 4 q^{7} - 732 q^{8} + 14265 q^{9} - 150 q^{10} + 2224 q^{12} + 14 q^{13} - 2484 q^{14} + 1000 q^{15} + 44724 q^{16} + 2634 q^{17} - 6618 q^{18} + 852 q^{19} + 3100 q^{20} + 640 q^{21} + 1088 q^{23} - 8584 q^{24} + 113125 q^{25} + 22436 q^{26} + 2320 q^{27} + 23556 q^{28} - 9594 q^{29} + 7800 q^{30} - 5468 q^{31} - 51256 q^{32} + 34056 q^{34} - 7900 q^{35} + 226264 q^{36} + 30142 q^{37} - 11580 q^{38} + 25248 q^{39} - 12600 q^{40} + 31666 q^{41} + 38924 q^{42} - 18928 q^{43} - 5675 q^{45} - 53336 q^{46} + 14956 q^{47} + 164940 q^{48} + 474889 q^{49} - 1250 q^{50} + 13536 q^{51} + 107836 q^{52} - 3286 q^{53} + 68456 q^{54} - 13328 q^{56} - 48160 q^{57} + 1076 q^{58} - 13976 q^{59} + 80900 q^{60} + 106230 q^{61} + 172672 q^{62} - 230740 q^{63} + 583052 q^{64} - 7250 q^{65} - 40004 q^{67} + 95748 q^{68} - 36648 q^{69} - 63200 q^{70} - 39828 q^{71} - 182316 q^{72} - 185134 q^{73} + 53204 q^{74} + 25000 q^{75} + 39728 q^{76} + 77212 q^{78} + 228688 q^{79} + 89600 q^{80} + 1028413 q^{81} - 300548 q^{82} - 345576 q^{83} + 514352 q^{84} - 88550 q^{85} - 21224 q^{86} - 24688 q^{87} - 268038 q^{89} + 50050 q^{90} + 418656 q^{91} - 222428 q^{92} + 953864 q^{93} - 193856 q^{94} - 117900 q^{95} + 711800 q^{96} + 280494 q^{97} + 436022 q^{98} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(605))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 11
605.6.a.a \(1\) \(97.032\) \(\Q\) None \(-2\) \(-4\) \(25\) \(-192\) \(-\) \(-\) \(q-2q^{2}-4q^{3}-28q^{4}+5^{2}q^{5}+8q^{6}+\cdots\)
605.6.a.b \(3\) \(97.032\) 3.3.21865.1 None \(7\) \(-36\) \(75\) \(102\) \(-\) \(-\) \(q+(2+\beta _{2})q^{2}+(-11-3\beta _{1})q^{3}+(12+\cdots)q^{4}+\cdots\)
605.6.a.c \(4\) \(97.032\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(5\) \(0\) \(-100\) \(90\) \(+\) \(-\) \(q+(1+\beta _{1})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(15+\beta _{1}+\cdots)q^{4}+\cdots\)
605.6.a.d \(5\) \(97.032\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-9\) \(0\) \(125\) \(-70\) \(-\) \(-\) \(q+(-2+\beta _{1})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(24+\cdots)q^{4}+\cdots\)
605.6.a.e \(6\) \(97.032\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-3\) \(0\) \(-150\) \(66\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(20+\cdots)q^{4}+\cdots\)
605.6.a.f \(7\) \(97.032\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(-27\) \(175\) \(-133\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(-4-\beta _{3})q^{3}+(15+\beta _{2}+\cdots)q^{4}+\cdots\)
605.6.a.g \(7\) \(97.032\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(1\) \(-27\) \(175\) \(133\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(-4-\beta _{3})q^{3}+(15+\beta _{2}+\cdots)q^{4}+\cdots\)
605.6.a.h \(8\) \(97.032\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-200\) \(0\) \(+\) \(+\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(13+\beta _{4})q^{4}-5^{2}q^{5}+\cdots\)
605.6.a.i \(9\) \(97.032\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-1\) \(9\) \(-225\) \(71\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3})q^{3}+(14-\beta _{1}+\cdots)q^{4}+\cdots\)
605.6.a.j \(9\) \(97.032\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(1\) \(9\) \(-225\) \(-71\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{3})q^{3}+(14-\beta _{1}+\cdots)q^{4}+\cdots\)
605.6.a.k \(10\) \(97.032\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(36\) \(250\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(4-\beta _{2})q^{3}+(3^{3}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
605.6.a.l \(14\) \(97.032\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(-18\) \(-350\) \(0\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(3+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
605.6.a.m \(18\) \(97.032\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(54\) \(450\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(3-\beta _{3})q^{3}+(21+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
605.6.a.n \(20\) \(97.032\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-17\) \(22\) \(500\) \(-559\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+(1-\beta _{3})q^{3}+(13-\beta _{1}+\cdots)q^{4}+\cdots\)
605.6.a.o \(20\) \(97.032\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-1\) \(0\) \(-500\) \(167\) \(+\) \(-\) \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(20+\beta _{2})q^{4}-5^{2}q^{5}+\cdots\)
605.6.a.p \(20\) \(97.032\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(1\) \(0\) \(-500\) \(-167\) \(+\) \(+\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(20+\beta _{2})q^{4}-5^{2}q^{5}+\cdots\)
605.6.a.q \(20\) \(97.032\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(17\) \(22\) \(500\) \(559\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(1-\beta _{3})q^{3}+(13-\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(605))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(605)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)