Properties

Label 5915.2.a
Level $5915$
Weight $2$
Character orbit 5915.a
Rep. character $\chi_{5915}(1,\cdot)$
Character field $\Q$
Dimension $310$
Newform subspaces $42$
Sturm bound $1456$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 5915 = 5 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5915.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 42 \)
Sturm bound: \(1456\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5915))\).

Total New Old
Modular forms 756 310 446
Cusp forms 701 310 391
Eisenstein series 55 0 55

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

\(5\)\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(37\)
\(+\)\(+\)\(-\)\(-\)\(42\)
\(+\)\(-\)\(+\)\(-\)\(40\)
\(+\)\(-\)\(-\)\(+\)\(36\)
\(-\)\(+\)\(+\)\(-\)\(47\)
\(-\)\(+\)\(-\)\(+\)\(30\)
\(-\)\(-\)\(+\)\(+\)\(30\)
\(-\)\(-\)\(-\)\(-\)\(48\)
Plus space\(+\)\(133\)
Minus space\(-\)\(177\)

Trace form

\( 310 q - 4 q^{2} - 4 q^{3} + 304 q^{4} + 4 q^{6} - 2 q^{7} + 300 q^{9} + O(q^{10}) \) \( 310 q - 4 q^{2} - 4 q^{3} + 304 q^{4} + 4 q^{6} - 2 q^{7} + 300 q^{9} - 4 q^{10} - 2 q^{11} - 2 q^{14} - 2 q^{15} + 284 q^{16} - 12 q^{17} - 8 q^{18} - 24 q^{19} + 2 q^{21} - 20 q^{22} + 16 q^{23} + 16 q^{24} + 310 q^{25} + 20 q^{27} - 14 q^{28} + 2 q^{29} + 20 q^{30} + 4 q^{31} + 16 q^{32} - 36 q^{33} - 4 q^{34} + 4 q^{35} + 292 q^{36} - 24 q^{37} + 16 q^{38} - 24 q^{40} - 28 q^{41} + 4 q^{42} - 12 q^{43} + 36 q^{44} + 8 q^{45} + 8 q^{46} + 28 q^{47} + 40 q^{48} + 310 q^{49} - 4 q^{50} - 6 q^{51} - 12 q^{53} + 44 q^{54} + 8 q^{55} - 6 q^{56} - 20 q^{57} + 52 q^{58} + 36 q^{59} - 4 q^{60} - 40 q^{61} + 64 q^{62} - 18 q^{63} + 300 q^{64} + 100 q^{66} - 44 q^{67} + 48 q^{68} + 36 q^{69} - 2 q^{70} - 16 q^{71} + 80 q^{72} - 80 q^{73} + 88 q^{74} - 4 q^{75} + 10 q^{79} + 32 q^{80} + 270 q^{81} + 88 q^{82} - 32 q^{83} + 36 q^{84} - 14 q^{85} + 64 q^{86} + 28 q^{87} + 32 q^{88} + 48 q^{89} + 88 q^{92} + 36 q^{93} + 36 q^{94} + 20 q^{95} + 144 q^{96} - 20 q^{97} - 4 q^{98} + 60 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5915))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 7 13
5915.2.a.a 5915.a 1.a $1$ $47.232$ \(\Q\) None \(-2\) \(0\) \(1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-q^{7}-3q^{9}-2q^{10}+\cdots\)
5915.2.a.b 5915.a 1.a $1$ $47.232$ \(\Q\) None \(-2\) \(1\) \(1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-q^{7}+\cdots\)
5915.2.a.c 5915.a 1.a $1$ $47.232$ \(\Q\) None \(-2\) \(3\) \(-1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+2q^{4}-q^{5}-6q^{6}+\cdots\)
5915.2.a.d 5915.a 1.a $1$ $47.232$ \(\Q\) None \(-1\) \(0\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}+q^{7}+3q^{8}-3q^{9}+\cdots\)
5915.2.a.e 5915.a 1.a $1$ $47.232$ \(\Q\) None \(-1\) \(1\) \(-1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
5915.2.a.f 5915.a 1.a $1$ $47.232$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{5}-q^{7}-2q^{9}+3q^{11}+\cdots\)
5915.2.a.g 5915.a 1.a $1$ $47.232$ \(\Q\) None \(1\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-3q^{9}+\cdots\)
5915.2.a.h 5915.a 1.a $1$ $47.232$ \(\Q\) None \(1\) \(1\) \(1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
5915.2.a.i 5915.a 1.a $1$ $47.232$ \(\Q\) None \(2\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}+q^{7}-3q^{9}-2q^{10}+\cdots\)
5915.2.a.j 5915.a 1.a $1$ $47.232$ \(\Q\) None \(2\) \(1\) \(-1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}+q^{7}+\cdots\)
5915.2.a.k 5915.a 1.a $1$ $47.232$ \(\Q\) None \(2\) \(3\) \(1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+2q^{4}+q^{5}+6q^{6}+\cdots\)
5915.2.a.l 5915.a 1.a $2$ $47.232$ \(\Q(\sqrt{17}) \) None \(1\) \(-1\) \(-2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{3}+(2+\beta )q^{4}-q^{5}+\cdots\)
5915.2.a.m 5915.a 1.a $4$ $47.232$ 4.4.1957.1 None \(-3\) \(4\) \(-4\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1}-\beta _{2})q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+\cdots\)
5915.2.a.n 5915.a 1.a $4$ $47.232$ 4.4.12197.1 None \(1\) \(0\) \(4\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
5915.2.a.o 5915.a 1.a $5$ $47.232$ 5.5.36497.1 None \(0\) \(-3\) \(-5\) \(-5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{3}+\beta _{4})q^{2}+(\beta _{2}+\beta _{4})q^{3}+\cdots\)
5915.2.a.p 5915.a 1.a $5$ $47.232$ 5.5.36497.1 None \(0\) \(-3\) \(5\) \(5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}+\beta _{3}-\beta _{4})q^{2}+(\beta _{2}+\beta _{4})q^{3}+\cdots\)
5915.2.a.q 5915.a 1.a $5$ $47.232$ 5.5.81589.1 None \(0\) \(-2\) \(-5\) \(5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
5915.2.a.r 5915.a 1.a $5$ $47.232$ 5.5.81589.1 None \(0\) \(-2\) \(5\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
5915.2.a.s 5915.a 1.a $5$ $47.232$ 5.5.144209.1 None \(0\) \(-1\) \(-5\) \(-5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}-q^{5}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
5915.2.a.t 5915.a 1.a $5$ $47.232$ 5.5.144209.1 None \(0\) \(-1\) \(5\) \(5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+q^{5}+(\beta _{3}+\cdots)q^{6}+\cdots\)
5915.2.a.u 5915.a 1.a $6$ $47.232$ 6.6.45853772.1 None \(-3\) \(0\) \(-6\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots\)
5915.2.a.v 5915.a 1.a $6$ $47.232$ 6.6.3728753.1 None \(-2\) \(-1\) \(6\) \(-6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{5}q^{2}+(-1-\beta _{1}-\beta _{2}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
5915.2.a.w 5915.a 1.a $6$ $47.232$ 6.6.3728753.1 None \(2\) \(-1\) \(-6\) \(6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{2}+(\beta _{1}+\beta _{4})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
5915.2.a.x 5915.a 1.a $7$ $47.232$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(0\) \(-7\) \(7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
5915.2.a.y 5915.a 1.a $7$ $47.232$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-1\) \(-7\) \(7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5915.2.a.z 5915.a 1.a $7$ $47.232$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-1\) \(7\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5915.2.a.ba 5915.a 1.a $7$ $47.232$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(7\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(2+\beta _{1}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
5915.2.a.bb 5915.a 1.a $7$ $47.232$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(1\) \(0\) \(7\) \(-7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)
5915.2.a.bc 5915.a 1.a $9$ $47.232$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(2\) \(-9\) \(-9\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5915.2.a.bd 5915.a 1.a $9$ $47.232$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(2\) \(9\) \(9\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5915.2.a.be 5915.a 1.a $10$ $47.232$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-4\) \(-10\) \(10\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{3}+\beta _{6}+\beta _{9})q^{4}+\cdots\)
5915.2.a.bf 5915.a 1.a $10$ $47.232$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-4\) \(10\) \(-10\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{3}+\beta _{6}+\beta _{9})q^{4}+\cdots\)
5915.2.a.bg 5915.a 1.a $15$ $47.232$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-7\) \(-7\) \(15\) \(15\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
5915.2.a.bh 5915.a 1.a $15$ $47.232$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-2\) \(-6\) \(-15\) \(15\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{14}q^{3}+(2-\beta _{10}+\beta _{11}+\cdots)q^{4}+\cdots\)
5915.2.a.bi 5915.a 1.a $15$ $47.232$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-1\) \(5\) \(15\) \(-15\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5915.2.a.bj 5915.a 1.a $15$ $47.232$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(1\) \(5\) \(-15\) \(15\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5915.2.a.bk 5915.a 1.a $15$ $47.232$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(2\) \(-6\) \(15\) \(-15\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{14}q^{3}+(2-\beta _{10}+\beta _{11}+\cdots)q^{4}+\cdots\)
5915.2.a.bl 5915.a 1.a $15$ $47.232$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(7\) \(-7\) \(-15\) \(-15\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
5915.2.a.bm 5915.a 1.a $18$ $47.232$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(4\) \(-18\) \(-18\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5915.2.a.bn 5915.a 1.a $18$ $47.232$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(4\) \(18\) \(18\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5915.2.a.bo 5915.a 1.a $21$ $47.232$ None \(-4\) \(5\) \(-21\) \(-21\) $+$ $+$ $+$ $\mathrm{SU}(2)$
5915.2.a.bp 5915.a 1.a $21$ $47.232$ None \(4\) \(5\) \(21\) \(21\) $-$ $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5915))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5915)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(455))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(845))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\)\(^{\oplus 2}\)